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TRIANGULAR MATRIX

  • Triangular matrix
  • Special kind of square matrix

    In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal

    Triangular matrix

    Triangular_matrix

  • Block matrix
  • Matrix defined using smaller matrices called blocks

    In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices

    Block matrix

    Block matrix

    Block_matrix

  • Matrix (mathematics)
  • Array of numbers

    called an upper triangular matrix. Similarly, if all entries of A above the main diagonal are zero, A is called a lower triangular matrix. If all entries

    Matrix (mathematics)

    Matrix (mathematics)

    Matrix_(mathematics)

  • Normal matrix
  • Matrix that commutes with its conjugate transpose

    } Proposition—A normal triangular matrix is diagonal. Proof Let A be any normal upper triangular matrix. Since ( A ∗ A ) i i = ( A A ∗ ) i

    Normal matrix

    Normal_matrix

  • Triangular matrix ring
  • In algebra, a triangular matrix ring, also called a triangular ring, is a ring constructed from two rings and a bimodule. If T {\displaystyle T} and U

    Triangular matrix ring

    Triangular_matrix_ring

  • Hessenberg matrix
  • Kind of square matrix in linear algebra

    algebra, a Hessenberg matrix is a special kind of square matrix, one that is "almost" triangular. To be exact, an upper Hessenberg matrix has zero entries

    Hessenberg matrix

    Hessenberg_matrix

  • Eigenvalues and eigenvectors
  • Concepts from linear algebra

    of these vectors. A matrix whose elements above the main diagonal are all zero is called a lower triangular matrix, while a matrix whose elements below

    Eigenvalues and eigenvectors

    Eigenvalues_and_eigenvectors

  • Definite matrix
  • Property of a mathematical matrix

    positive definiteness of a symmetric real matrix. Namely, the matrix is reduced to an upper triangular matrix by using elementary row operations, as in

    Definite matrix

    Definite_matrix

  • Crout matrix decomposition
  • Type of matrix factorization

    the Crout matrix decomposition is an LU decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and,

    Crout matrix decomposition

    Crout_matrix_decomposition

  • Schur decomposition
  • Matrix factorisation in mathematics

    Schur, is a matrix decomposition. It allows one to write an arbitrary complex square matrix as unitarily similar to an upper triangular matrix whose diagonal

    Schur decomposition

    Schur_decomposition

  • Square matrix
  • Matrix with the same number of rows and columns

    diagonal matrix. If all entries below (resp. above) the main diagonal are zero, A {\displaystyle A} is called an upper (resp. lower) triangular matrix. The

    Square matrix

    Square matrix

    Square_matrix

  • QR decomposition
  • Matrix decomposition

    factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used

    QR decomposition

    QR_decomposition

  • Matrix decomposition
  • Representation of a matrix as a product

    decomposition. The LU decomposition factorizes a matrix into a lower triangular matrix L and an upper triangular matrix U. The systems L ( U x ) = b {\displaystyle

    Matrix decomposition

    Matrix decomposition

    Matrix_decomposition

  • Determinant
  • In mathematics, invariant of square matrices

    determinants, and the determinant of a triangular matrix is the product of its diagonal entries. The determinant of a 2 × 2 matrix is | a b c d | = a d − b c ,

    Determinant

    Determinant

  • Cholesky decomposition
  • Matrix decomposition method

    decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for

    Cholesky decomposition

    Cholesky_decomposition

  • Toeplitz matrix
  • Matrix with shifting rows

    triangular Toeplitz matrices and C {\displaystyle C} is a strictly lower triangular matrix. The convolution operation can be constructed as a matrix multiplication

    Toeplitz matrix

    Toeplitz_matrix

  • LU decomposition
  • Type of matrix factorization

    factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix multiplication and matrix decomposition)

    LU decomposition

    LU_decomposition

  • Band matrix
  • Matrix with non-zero elements only in a diagonal band

    a pentadiagonal matrix and so on. Triangular matrices For k1 = 0, k2 = n−1, one obtains the definition of an upper triangular matrix similarly, for k1

    Band matrix

    Band_matrix

  • Symmetric matrix
  • Matrix equal to its transpose

    In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, A  is symmetric ⟺ A = A T . {\displaystyle A{\text{

    Symmetric matrix

    Symmetric matrix

    Symmetric_matrix

  • Square root of a matrix
  • Mathematical operation

    of a triangular matrix are precisely its eigenvalues (see Triangular matrix#Properties). An n × n matrix A is diagonalizable if there is a matrix V and

    Square root of a matrix

    Square_root_of_a_matrix

  • QR algorithm
  • Algorithm to calculate eigenvalues

    perform a QR decomposition, writing the matrix as a product of an orthogonal matrix and an upper triangular matrix, multiply the factors in the reverse order

    QR algorithm

    QR_algorithm

  • Factorization
  • (Mathematical) decomposition into a product

    many kinds of matrix factorizations. For example, every matrix has a unique LUP factorization as a product of a lower triangular matrix L with all diagonal

    Factorization

    Factorization

    Factorization

  • Gram–Schmidt process
  • Orthonormalization of a set of vectors

    vectors of a full column rank matrix yields the QR decomposition (it is decomposed into an orthogonal and a triangular matrix). The vector projection of

    Gram–Schmidt process

    Gram–Schmidt process

    Gram–Schmidt_process

  • Condition number
  • Function's sensitivity to argument change

    _{i}{\big (}|a_{ii}|{\big )}}}} recalling that the eigenvalues of any triangular matrix are simply the diagonal entries. The condition number computed with

    Condition number

    Condition_number

  • Eigenvalue algorithm
  • Numerical methods for matrix eigenvalue calculation

    possible for a real or complex matrix to have all real eigenvalues without being Hermitian. For example, a real triangular matrix has its eigenvalues along

    Eigenvalue algorithm

    Eigenvalue_algorithm

  • Generalized minimal residual method
  • Method for numerical solution of certain systems of equations

    decomposition: find an (n + 1)-by-(n + 1) orthogonal matrix Ωn and an (n + 1)-by-n upper triangular matrix R ~ n {\displaystyle {\tilde {R}}_{n}} such that

    Generalized minimal residual method

    Generalized_minimal_residual_method

  • Numerical linear algebra
  • Field of mathematics

    matrix A consists of a lower triangular matrix L and an upper triangular matrix U so that A = LU. The matrix U is found by an upper triangularization

    Numerical linear algebra

    Numerical_linear_algebra

  • Iwasawa decomposition
  • Mathematical process dealing with Lie groups

    generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix (QR decomposition, a consequence

    Iwasawa decomposition

    Iwasawa_decomposition

  • Incomplete Cholesky factorization
  • Approximation of a matrix's Cholesky factorization

    definite matrix A of order N is A = LL* where L is a lower triangular matrix. An incomplete Cholesky factorization is given by a lower triangular matrix K that

    Incomplete Cholesky factorization

    Incomplete_Cholesky_factorization

  • Characteristic polynomial
  • Polynomial whose roots are the eigenvalues of a matrix

    algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It

    Characteristic polynomial

    Characteristic_polynomial

  • Diagonalizable matrix
  • Matrices similar to diagonal matrices

    norm. Note that n ≥ 2 {\displaystyle n\geq 2} Defective matrix Scaling (geometry) Triangular matrix Semisimple operator Diagonalizable group Jordan normal

    Diagonalizable matrix

    Diagonalizable_matrix

  • Block LU decomposition
  • Type of matrix factorization

    decomposition is a matrix decomposition of a block matrix into a lower block triangular matrix L and an upper block triangular matrix U. This decomposition

    Block LU decomposition

    Block_LU_decomposition

  • Complete orthogonal decomposition
  • {\displaystyle T} is a triangular matrix. For a matrix A {\displaystyle A} of rank r {\displaystyle r} , the triangular matrix T {\displaystyle T} can

    Complete orthogonal decomposition

    Complete_orthogonal_decomposition

  • Vandermonde matrix
  • Matrix of geometric progressions

    In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row:

    Vandermonde matrix

    Vandermonde_matrix

  • LAPACK
  • Software library for numerical linear algebra

    value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. The routines

    LAPACK

    LAPACK

    LAPACK

  • Eigendecomposition of a matrix
  • Matrix decomposition

    Cholesky decomposition, where L {\displaystyle \mathbf {L} } is a lower triangular matrix. Orthogonal matrices satisfy Q Q T = I {\displaystyle \mathbf {Q}

    Eigendecomposition of a matrix

    Eigendecomposition_of_a_matrix

  • Adjacency matrix
  • Square matrix used to represent a graph or network

    computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices

    Adjacency matrix

    Adjacency_matrix

  • Basic Linear Algebra Subprograms
  • Routines for performing common linear algebra operations

    routines. For example, a library may include a program to solve a matrix that is upper triangular. The libraries would include single-precision and double-precision

    Basic Linear Algebra Subprograms

    Basic_Linear_Algebra_Subprograms

  • Pascal matrix
  • Infinite matrices with Pascal's triangle as elements

    triangle in matrix form. There are three natural ways to achieve this: as a lower-triangular matrix, an upper-triangular matrix, or a symmetric matrix. For example

    Pascal matrix

    Pascal_matrix

  • Polynomial matrix spectral factorization
  • A=LL^{*}} where L {\displaystyle L} is a lower triangular matrix. If we don't restrict to lower triangular matrices we can consider all factorizations of

    Polynomial matrix spectral factorization

    Polynomial_matrix_spectral_factorization

  • Numerical methods for linear least squares
  • } , where Q is an m×m orthogonal matrix (QTQ=I) and R is an n×n upper triangular matrix with r i i > 0 {\displaystyle r_{ii}>0} . The residual

    Numerical methods for linear least squares

    Numerical_methods_for_linear_least_squares

  • Jabotinsky matrix
  • B ( f ) {\displaystyle \mathbf {B} (f)} becomes an infinite lower triangular matrix whose entries are given by ordinary Bell polynomials evaluated at

    Jabotinsky matrix

    Jabotinsky_matrix

  • Nest algebra
  • algebras are a class of operator algebras that generalise the upper-triangular matrix algebras to a Hilbert space context. They were introduced by Ringrose (1965)

    Nest algebra

    Nest_algebra

  • Schur complement
  • Tool in linear algebra and matrix analysis

    on the matrix M. In order to eliminate the elements below the block diagonal, one multiplies the matrix M by a block lower triangular matrix on the right

    Schur complement

    Schur_complement

  • Computational complexity of mathematical operations
  • Algorithmic runtime requirements for common math procedures

    Bunch, James R.; Hopcroft, John E. (1974). "Triangular Factorization and Inversion by Fast Matrix Multiplication". Mathematics of Computation. 28

    Computational complexity of mathematical operations

    Computational complexity of mathematical operations

    Computational_complexity_of_mathematical_operations

  • Matrix ring
  • Mathematical ring whose elements are matrices

    abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication. The set

    Matrix ring

    Matrix_ring

  • Stirling number
  • Mathematical sequences in combinatorics

    understood to be matrix inverse relationships. That is, let s be the lower triangular matrix of Stirling numbers of the first kind, whose matrix elements s

    Stirling number

    Stirling_number

  • Irreducibility (mathematics)
  • Index of articles associated with the same name

    irreducible topological space. A matrix is irreducible if it is not similar via a permutation to a block upper triangular matrix (that has more than one block

    Irreducibility (mathematics)

    Irreducibility_(mathematics)

  • Trace (linear algebra)
  • Sum of elements on the main diagonal

    from the fact that A is always similar to its Jordan form, an upper triangular matrix having λ1, ..., λn on the main diagonal, together with the similarity-invariance

    Trace (linear algebra)

    Trace_(linear_algebra)

  • Row echelon form
  • Possible form of a matrix

    and a matrix in row echelon form is (weakly) upper triangular. Thus, the row echelon form can be viewed as a generalization of upper triangular form for

    Row echelon form

    Row echelon form

    Row_echelon_form

  • Nilpotent matrix
  • Mathematical concept in algebra

    triangular matrix with zeros along the main diagonal is nilpotent, with index ≤ n {\displaystyle \leq n} [citation needed]. For example, the matrix B

    Nilpotent matrix

    Nilpotent_matrix

  • Givens rotation
  • Concept in numerical linear algebra

    from above) yield an upper triangular matrix in order to compute the QR decomposition. In order to form the desired matrix, zeroing elements (2,1) and

    Givens rotation

    Givens_rotation

  • List of named matrices
  • matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries

    List of named matrices

    List of named matrices

    List_of_named_matrices

  • Attention (machine learning)
  • Machine learning technique

    {\displaystyle M\in \mathbb {R} ^{n\times n}} is a strictly upper triangular matrix, with zeros on and below the diagonal and − ∞ {\displaystyle -\infty

    Attention (machine learning)

    Attention (machine learning)

    Attention_(machine_learning)

  • Orthogonal matrix
  • Real square matrix whose columns and rows are orthogonal unit vectors

    In linear algebra, an orthogonal matrix or orthonormal matrix Q, is a real-valued square matrix whose columns and rows are orthonormal vectors. One way

    Orthogonal matrix

    Orthogonal_matrix

  • Hermitian matrix
  • Matrix equal to its conjugate-transpose

    In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose

    Hermitian matrix

    Hermitian_matrix

  • Outline of linear algebra
  • matrix Pfaffian Projection Spectral theorem Perron–Frobenius theorem List of matrices Diagonal matrix, main diagonal Diagonalizable matrix Triangular

    Outline of linear algebra

    Outline_of_linear_algebra

  • Jordan matrix
  • Block diagonal matrix of Jordan blocks

    the mathematical discipline of matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring R (whose identities

    Jordan matrix

    Jordan_matrix

  • Richardson extrapolation
  • Sequence acceleration method in numerical analysis

    computation. A = zeroMatrix(maxRows, maxRows) % Compute the top left element of the matrix. % The first row of this (lower triangular) matrix has now been filled

    Richardson extrapolation

    Richardson extrapolation

    Richardson_extrapolation

  • Moore–Penrose inverse
  • Most widely known generalized inverse of a matrix

    A^{+}} ⁠ of a matrix ⁠ A {\displaystyle A} ⁠, often called the pseudoinverse, is the most widely known generalization of the inverse matrix. It was independently

    Moore–Penrose inverse

    Moore–Penrose_inverse

  • Solvable group
  • Group with subnormal series where all factors are abelian

    {\displaystyle n\times n} upper triangular matrix and S {\displaystyle S} is a m × m {\displaystyle m\times m} upper triangular matrix. Any finite group whose

    Solvable group

    Solvable group

    Solvable_group

  • Lie group decomposition
  • elimination, which generically writes a matrix as the product of an upper triangular matrix with a lower triangular matrix—but with exceptional cases. It is

    Lie group decomposition

    Lie_group_decomposition

  • Diagonal matrix
  • Matrix whose only nonzero elements are on its main diagonal

    both upper- and lower-triangular. A diagonal matrix is symmetric. The identity matrix In and zero matrix are diagonal. A 1×1 matrix is always diagonal.

    Diagonal matrix

    Diagonal_matrix

  • Kalman filter
  • Algorithm that estimates unknowns from a series of measurements over time

    decomposition form, P = U·D·UT, where U is a unit triangular matrix (with unit diagonal), and D is a diagonal matrix. Between the two, the U-D factorization uses

    Kalman filter

    Kalman filter

    Kalman_filter

  • Singular value decomposition
  • Matrix decomposition

    then it is advantageous to first reduce the matrix ⁠ M {\displaystyle \mathbf {M} } ⁠ to a triangular matrix with the QR decomposition and then use Householder

    Singular value decomposition

    Singular value decomposition

    Singular_value_decomposition

  • Runge–Kutta methods
  • Family of implicit and explicit iterative methods

    the Butcher tableau: the coefficient matrix a i j {\displaystyle a_{ij}} of an explicit method is lower triangular. In an implicit method, the sum over

    Runge–Kutta methods

    Runge–Kutta methods

    Runge–Kutta_methods

  • Triangulation (disambiguation)
  • Topics referred to by the same term

    2023 Schur triangulation, a process of finding an upper triangular matrix similar to a given matrix Stellar triangulation, a method of geodesy which uses

    Triangulation (disambiguation)

    Triangulation_(disambiguation)

  • Incomplete LU factorization
  • Concept in numerical linear algebra

    because the matrices are triangular. For a typical sparse matrix, the LU factors can be much less sparse than the original matrix — a phenomenon called fill-in

    Incomplete LU factorization

    Incomplete_LU_factorization

  • Matrix exponential
  • Matrix operation generalizing exponentiation of scalar numbers

    In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems

    Matrix exponential

    Matrix_exponential

  • Jordan normal form
  • Form of a matrix indicating its eigenvalues and their algebraic multiplicities

    the matrix; they need not be distinct. In linear algebra, a Jordan normal form, also known as a Jordan canonical form, is an upper triangular matrix of

    Jordan normal form

    Jordan_normal_form

  • Adjugate matrix
  • For a square matrix, the transpose of the cofactor matrix

    classical adjoint adj(A) of a square matrix A is the transpose of its cofactor matrix. It is occasionally known as adjunct matrix, or "adjoint", though that normally

    Adjugate matrix

    Adjugate_matrix

  • List of inventions and discoveries by women
  • perform a QR decomposition, writing the matrix as a product of an orthogonal matrix and an upper triangular matrix, multiply the factors in the reverse order

    List of inventions and discoveries by women

    List_of_inventions_and_discoveries_by_women

  • Iterative proportional fitting
  • Estimates values in an N-dimensional matrix

    Thus, a bloc-diagonal matrix is projected as a bloc-diagonal matrix and a triangular matrix is projected as a triangular matrix. Theorem of separable

    Iterative proportional fitting

    Iterative_proportional_fitting

  • Riordan array
  • A Riordan array is an infinite lower triangular matrix, D {\displaystyle D} , constructed from two formal power series, d ( t ) {\displaystyle d(t)} of

    Riordan array

    Riordan_array

  • Hereditary ring
  • Ring whose ideals are projective

    resolution (which is of length 1) for modules over a path algebra. The triangular matrix ring [ Z Q 0 Q ] {\displaystyle {\begin{bmatrix}\mathbb {Z} &\mathbb

    Hereditary ring

    Hereditary_ring

  • Conjugate gradient method
  • Mathematical optimization algorithm

    factorization. The resulting matrix is the lower triangular matrix L {\displaystyle \mathbf {L} } , and the preconditioner matrix is: M = L L T {\displaystyle

    Conjugate gradient method

    Conjugate gradient method

    Conjugate_gradient_method

  • Probability density function
  • Description of continuous random distribution

    _{n\times 1}&\mathbf {I} _{n\times n}\end{bmatrix}},} which is an upper triangular matrix with ones on the main diagonal, therefore its determinant is 1. Applying

    Probability density function

    Probability density function

    Probability_density_function

  • Quadratic unconstrained binary optimization
  • Combinatorial optimization problem

    N {\displaystyle n\in \mathbb {N} } . Given a symmetric or upper triangular matrix Q ∈ R n × n {\displaystyle {\boldsymbol {Q}}\in \mathbb {R} ^{n\times

    Quadratic unconstrained binary optimization

    Quadratic_unconstrained_binary_optimization

  • List of numerical analysis topics
  • analysis: Sparse matrix Band matrix Bidiagonal matrix Tridiagonal matrix Pentadiagonal matrix Skyline matrix Circulant matrix Triangular matrix Diagonally dominant

    List of numerical analysis topics

    List_of_numerical_analysis_topics

  • Spectral theorem
  • Result about when a matrix can be diagonalized

    triangular matrix is diagonal (see normal matrix). The converse is obvious. In other words, A is normal if and only if there exists a unitary matrix U

    Spectral theorem

    Spectral_theorem

  • Divided differences
  • Algorithm for computing polynomial coefficients

    x_{k}} 's. The divided difference scheme can be put into an upper triangular matrix: T f ( x 0 , … , x n ) = ( f [ x 0 ] f [ x 0 , x 1 ] f [ x 0 , x 1

    Divided differences

    Divided_differences

  • Block reflector
  • elementary reflectors. It is also referred to as a triangular factor, and is a triangular matrix and they are used in the Householder transformation

    Block reflector

    Block_reflector

  • Gaussian ensemble
  • Random matrix with gaussian entries

    i {\displaystyle H_{i}} is a Householder matrix, and R N {\displaystyle R_{N}} is an upper triangular matrix with independent entries, such that each

    Gaussian ensemble

    Gaussian_ensemble

  • E8 lattice
  • Lattice in 8-dimensional space with special properties

    One possible basis for Γ8 is given by the columns of the (upper triangular) matrix [ 2 − 1 0 0 0 0 0 1 / 2 0 1 − 1 0 0 0 0 1 / 2 0 0 1 − 1 0 0 0 1 /

    E8 lattice

    E8_lattice

  • Variance decomposition of forecast errors
  • that element of the matrix Θ i = Φ i P , {\displaystyle \Theta _{i}=\Phi _{i}P,} where P {\displaystyle P} is a lower triangular matrix obtained by a Cholesky

    Variance decomposition of forecast errors

    Variance_decomposition_of_forecast_errors

  • Faulhaber's formula
  • Expression for sums of powers

    {1}{2}}\right)}{p+1}}} Furthermore, given the lower triangular matrix [ G ( h , d ) ] r , c := { 0 if  c > r d r − 1 r ( r c ) B r − c (

    Faulhaber's formula

    Faulhaber's_formula

  • Invariant subspace
  • Subspace preserved by a linear mapping

    family in L(V) can be simultaneously upper-triangularized. To see this, note that an upper-triangular matrix representation corresponds to a flag of invariant

    Invariant subspace

    Invariant_subspace

  • Generalized eigenvector
  • Vector satisfying some of the criteria of an eigenvector

    algebra, a generalized eigenvector of an n × n {\displaystyle n\times n} matrix A {\displaystyle A} is a vector which satisfies certain criteria which are

    Generalized eigenvector

    Generalized_eigenvector

  • Packed storage matrix
  • Programming term

    matrix. Typical examples of matrices that can take advantage of packed storage include: symmetric or hermitian matrix Triangular matrix Banded matrix

    Packed storage matrix

    Packed_storage_matrix

  • Linear recurrence with constant coefficients
  • Mathematical relation defining a sequence

    equation. In the homogeneous case yi is a para-permanent of a lower triangular matrix The recurrence y t = a 1 y t − 1 + ⋯ + a n y t − n + b , {\displaystyle

    Linear recurrence with constant coefficients

    Linear_recurrence_with_constant_coefficients

  • Footwork (martial arts)
  • Concept in martial arts

    slide." The fighter will first move to the desired 'point' on the triangular matrix, then swiftly slide one's rear leg to meet his leading foot. From

    Footwork (martial arts)

    Footwork (martial arts)

    Footwork_(martial_arts)

  • Global dimension
  • Concept in ring theory and homological algebra

    global dimensions and the weak global dimension are all the same. The triangular matrix ring [ Z Q 0 Q ] {\displaystyle {\begin{bmatrix}\mathbb {Z} &\mathbb

    Global dimension

    Global_dimension

  • Overdetermined system
  • More equations than unknowns (mathematics)

    semi-orthonormal matrix that spans the range of the matrix A {\displaystyle A} , and where R {\displaystyle R} is a (small) square right-triangular matrix. The solution

    Overdetermined system

    Overdetermined_system

  • Permanent (mathematics)
  • Polynomial of the elements of a matrix

    their respective complements in that set. If A {\displaystyle A} is a triangular matrix, i.e., a i j = 0 {\displaystyle a_{ij}=0} whenever i > j {\displaystyle

    Permanent (mathematics)

    Permanent_(mathematics)

  • List of triangle topics
  • of Triangle Centers Pythagorean Triangles The Secrets of Triangles Triangular matrix (2,3,7) triangle group Bell numbers Boustrophedon transform Eulerian

    List of triangle topics

    List_of_triangle_topics

  • Conway polyhedron notation
  • Method of describing higher-order polyhedra

    The matrix for the composition of two operators is just the product of the matrixes for the two operators. Distinct operators may have the same matrix, for

    Conway polyhedron notation

    Conway polyhedron notation

    Conway_polyhedron_notation

  • Separation principle
  • d{bmatrix}}{\begin{bmatrix}x\\e\\\end{bmatrix}}.} Since this is a triangular matrix, the eigenvalues are just those of A − BK together with those of A − LC

    Separation principle

    Separation_principle

  • Matrix analysis
  • Study of matrices and their algebraic properties

    matrix P is called a similarity matrix, and is necessarily invertible. LU decomposition splits a matrix into a matrix product of an upper triangular matrix

    Matrix analysis

    Matrix_analysis

  • Representation theory of finite groups
  • Representations of finite groups, particularly on vector spaces

    A  is an upper triangular matrix } . {\displaystyle G=\{A\in {\text{GL}}_{2}(\mathbb {C} )|\,A\,\,{\text{ is an upper triangular matrix}}\}.} Together

    Representation theory of finite groups

    Representation_theory_of_finite_groups

  • Molecular phylogenetics
  • Branch of phylogeny that analyzes genetic, hereditary molecular differences

    between all pairs of samples have been determined, the resulting triangular matrix of differences is submitted to some form of statistical cluster analysis

    Molecular phylogenetics

    Molecular_phylogenetics

AI & ChatGPT searchs for online references containing TRIANGULAR MATRIX

TRIANGULAR MATRIX

AI search references containing TRIANGULAR MATRIX

TRIANGULAR MATRIX

  • Garton
  • Boy/Male

    English

    Garton

    Lives in the triangular farm stead.

    Garton

  • Garafeld
  • Boy/Male

    English

    Garafeld

    From the triangular field.

    Garafeld

  • Garland
  • Surname or Lastname

    English

    Garland

    English : metonymic occupational name for a maker of garlands or chaplets, perhaps also a habitational name from a house sign. The word is first attested in the 14th century, from Old French, and appears to be of Germanic origin.English : habitational name from a minor place, such as Garland in Chulmleigh, Devon, named from Old English gāra ‘triangular piece of land’ (see Gore) + land ‘cultivated land’, ‘estate’.

    Garland

  • Gordie
  • Boy/Male

    Anglo, Australian, British, English, French

    Gordie

    From the Cornered Hill; Hill Near Meadows; Triangular Hill

    Gordie

  • Garfield
  • Surname or Lastname

    English

    Garfield

    English : probably a habitational name from a lost or unidentified place, generally from a field name denoting a triangular area, Old English gāra (see Gore) at the corner of an open field after rectangular furlongs had been laid out.Jewish : Americanized form of one or more like-sounding Jewish surnames.U.S. President James Abram Garfield (1831–81) was preceded by at least six Garfields born in America, his immigrant ancestor having come to Massachusetts Bay with John Winthrop in 1630.

    Garfield

  • Gore
  • Surname or Lastname

    English

    Gore

    English : habitational name from any of various places, for example in Kent and Wiltshire, named Gore, from Old English gāra ‘triangular piece of land’ (a derivative of gār ‘spear’, with reference to the triangular shape of a spearhead).French : nickname for a gluttonous and idle individual, from Old French gore ‘sow’ (of allegedly imitative origin, reflecting the grunting of the animal).

    Gore

  • Garafeld
  • Boy/Male

    American, British, English

    Garafeld

    Battlefield; From the Triangular Field

    Garafeld

  • Gordon
  • Boy/Male

    American, Anglo, Australian, British, Chinese, Christian, Danish, English, French, German, Irish, Jamaican, Scottish

    Gordon

    Hill Near the Meadow; From the Cornered Hill; Triangular Hill; Large Fortification; From the Marshes; One of Scotland's Great Clans; Spacious Fort

    Gordon

  • Gore
  • Boy/Male

    British, English

    Gore

    Spear; Wedge-shaped Object; Triangular Shaped Piece of Land

    Gore

  • Garatun
  • Boy/Male

    American, British, English

    Garatun

    Lives in the Triangular Farm Stead

    Garatun

  • Delta
  • Girl/Female

    American, Australian, Christian, Greek, Hebrew

    Delta

    Triangular River Mouth; Mouth of a River; Fourth Letter of Greek Alphabet; A Name for a Fourth Child; Fourth Letter of the Greek Alphabet

    Delta

  • Garfield
  • Boy/Male

    African, American, Anglo, Australian, British, Christian, English, Jamaican

    Garfield

    Battlefield; Spear Field; Triangular Field

    Garfield

  • Garwood
  • Surname or Lastname

    English

    Garwood

    English : habitational name from a lost or unidentified minor place, possibly in East Anglia, where the name is most common, and probably so called from Old English gāra ‘gore’, ‘triangular piece of land’ + wudu ‘wood’.

    Garwood

  • Garfield
  • Boy/Male

    English American

    Garfield

    From the triangular field. From an Old English surname and place name, meaning 'field of spears'.

    Garfield

  • Garton
  • Surname or Lastname

    English

    Garton

    English : habitational name from Garton in East Yorkshire or from various minor places so named, from Old English gāra ‘triangular plot of land’ + tūn ‘farmstead’.

    Garton

  • Gorham
  • Surname or Lastname

    English (Kent)

    Gorham

    English (Kent) : apparently a habitational name from a lost or unidentified place, possibly so named from Old English gāra ‘triangular piece of land’ + hām ‘homestead’.Born in England, John Gorham emigrated to MA and in 1643 married Desire Howland, daughter of John Howland, who came to America on the Mayflower. His descendant Nathaniel (1738–96) was born in Charlestown, MA, and was one of the signers of the Declaration of Independence.

    Gorham

  • Gorden
  • Boy/Male

    American, Australian, British, Christian, English, German

    Gorden

    Hill Near Meadows; Triangular Hill; Spacious Fort

    Gorden

  • Garton
  • Boy/Male

    American, Anglo, Australian, British, English

    Garton

    From the Triangle Shaped Settlement; Lives in the Triangular Farm Stead

    Garton

  • Gordan
  • Boy/Male

    American, Anglo, Australian, British, Celtic, English, French, Gaelic, Irish, Scottish

    Gordan

    Hill Near the Meadow; Triangular Hill; Hero; Large Fortification; Fortress

    Gordan

  • GABLE
  • Male

    English

    GABLE

    English surname transferred to forename use, possibly originally a habitational name derived from a place named from Old Norse gafl, GABLE means "gable," a term used to denote a "triangular-shaped hill." 

    GABLE

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Online names & meanings

  • Ajithabh | அஜீதாப
  • Boy/Male

    Tamil

    Ajithabh | அஜீதாப

    One who has conquered the Sky, Victor

  • Chavi
  • Girl/Female

    Indian

    Chavi

    Ray of light

  • Justus
  • Boy/Male

    Latin Swedish American Biblical

    Justus

    Just.

  • Azbak
  • Boy/Male

    Arabic, Muslim

    Azbak

    Independent; Autonomous

  • Zakiyah |
  • Girl/Female

    Muslim

    Zakiyah |

    Intelligent

  • Yosepha
  • Girl/Female

    Hebrew

    Yosepha

    God will multiply.

  • Dorien
  • Boy/Male

    American, British, English, Greek

    Dorien

    Descendant of Dorus; Place Name; From Doris

  • Anirveda
  • Girl/Female

    Indian

    Anirveda

    Not caring sorrows and suffers

  • Jacen
  • Boy/Male

    Australian, Greek, Jamaican

    Jacen

    Healer; The Lord is Salvation

  • Kadamb
  • Boy/Male

    Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu

    Kadamb

    Name of a Tree

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Other words and meanings similar to

TRIANGULAR MATRIX

AI search in online dictionary sources & meanings containing TRIANGULAR MATRIX

TRIANGULAR MATRIX

  • Subtriangular
  • a.

    Nearly, but not perfectly, triangular.

  • Didal
  • n.

    A kind of triangular spade.

  • Scalene
  • a.

    Designating several triangular muscles called scalene muscles.

  • Triangularly
  • adv.

    In a triangular manner; in the form of a triangle.

  • Triangulate
  • v. t.

    To make triangular, or three-cornered.

  • Triangulated
  • imp. & p. p.

    of Triangulate

  • Biangulated
  • a.

    Biangular.

  • Gore
  • v.

    A small traingular piece of land.

  • Burr
  • n.

    A triangular chisel.

  • Deltoid
  • a.

    Shaped like the Greek / (delta); delta-shaped; triangular.

  • Triangular
  • a.

    Oblong or elongated, and having three lateral angles; as, a triangular seed, leaf, or stem.

  • Triangled
  • a.

    Having three angles; triangular.

  • Triangulating
  • p. pr. & vb. n.

    of Triangulate

  • Triangularity
  • n.

    The quality or state of being triangular.

  • Trigon
  • n.

    A kind of triangular lyre or harp.

  • Triangulares
  • n. pl.

    The triangular, or maioid, crabs. See Illust. under Maioid, and Illust. of Spider crab, under Spider.

  • Biangulous
  • a.

    Biangular.

  • Triangular
  • a.

    Having three angles; having the form of a triangle.

  • Hexoctahedron
  • n.

    A solid having forty-eight equal triangular faces.

  • Triangulate
  • v. t.

    To divide into triangles; specifically, to survey by means of a series of triangles properly laid down and measured.