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Linear operator used in quantum mechanics
In physics, particularly in quantum perturbation theory, the matrix element refers to the linear operator of a modified Hamiltonian using Dirac notation
Matrix_element_(physics)
Topics referred to by the same term
Matrix element may refer to: The (scalar) entries of a matrix. Matrix element (physics), the value of a linear operator (especially a modified Hamiltonian)
Matrix_element
Square matrix used to represent a graph or network
set U = {u1, ..., un}, the adjacency matrix is a square n × n matrix A such that its element Aij is 1 when there is an edge from vertex ui to vertex uj,
Adjacency_matrix
Array of numbers
In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and
Matrix_(mathematics)
Distinguished element of a Lie algebra's center
In mathematics, a Casimir element (also known as a Casimir invariant or Casimir operator) is a distinguished element of the center of the universal enveloping
Casimir_element
centroid of each element. The 2D element stiffness matrix size is 6 × 6; the components of the upper left quarter of the stiffness matrix are shown below:
Applied_element_method
Matrix equal to its conjugate-transpose
matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose; that is, if the element in
Hermitian_matrix
Numerical method for solving physical or engineering problems
dynamic implicit and explicit finite element simulations of the native knee joint" (PDF). Medical Engineering & Physics. 38 (10): 1123–1130. doi:10.1016/j
Finite_element_method
Matrix-valued random variable
probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries
Random_matrix
Formulation of quantum mechanics
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually
Matrix_mechanics
Matrix operation generalizing exponentiation of scalar numbers
t = 1. When X is an n × n diagonal matrix then exp(X) will be an n × n diagonal matrix with each diagonal element equal to the ordinary exponential applied
Matrix_exponential
Form of a matrix
diagonal elements of a skew-symmetric matrix are zeros because each element must be its own negative. The matrix A = [ 0 2 − 45 − 2 0 − 4 45 4 0 ] {\displaystyle
Skew-symmetric_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
Intrinsic quantum property of particles
first element imaginary and negative if there is a sign ambiguity. The present convention is used by software such as SymPy; while many physics textbooks
Spin_(physics)
Measure of covariance of components of a random vector
covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the
Covariance_matrix
Matrix describing continuous-time Markov chains
between states. In a transition-rate matrix Q {\displaystyle Q} (sometimes written A {\displaystyle A} ), element q i j {\displaystyle q_{ij}} (for i ≠
Transition-rate_matrix
Matrix representing the effect of scattering on a physical system
In physics, the S-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering
S-matrix
Mathematical operation in linear algebra
as well as in applied mathematics, statistics, physics, economics, and engineering. Computing matrix products is a central operation in all computational
Matrix_multiplication
Matrix representing a Euclidean rotation
rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [
Rotation_matrix
System for describing optical polarization
particular optical element is represented by a Mueller matrix—a 4×4 matrix that is an overlapping generalization of the Jones matrix. Disregarding coherent
Mueller_calculus
Four-dimensional number system
Mathematics, EMS Press, 2001 [1994] "Matrix and quaternion". Frequently Asked Questions. 1.21. Sweetser, Doug. "Doing physics with quaternions". Hoffman, Gernot
Quaternion
Matrix operation which flips a matrix over its diagonal
that flips a matrix over its diagonal; that is, transposition switches the row and column indices of the matrix A to produce another matrix, called the
Transpose
Most widely known generalized inverse of a matrix
a matrix, but sometimes applied to other elements of algebraic structures which share some but not all properties expected for an inverse element. A
Moore–Penrose_inverse
Matrix whose only nonzero elements are on its main diagonal
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices
Diagonal_matrix
Topics referred to by the same term
Unitary element Unitary group Unitary matrix Unitary morphism Unitary operator Unitary transformation Unitary representation Unitarity (physics) E-unitary
Unitary
Matrices similar to diagonal matrices
if there exists an n × n {\displaystyle n\times n} invertible matrix (i.e. an element of the general linear group GL ( n , F ) {\displaystyle \operatorname
Diagonalizable_matrix
Concepts from linear algebra
_{n}\end{bmatrix}}.} With this in mind, define the diagonal matrix Λ where each diagonal element Λii is the eigenvalue associated with the ith column of Q
Eigenvalues_and_eigenvectors
Matrix representation of a graph
theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation of a
Laplacian_matrix
Matrix used to describe the transitions of a Markov chain
It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov
Stochastic_matrix
Elements of a field, e.g. real numbers, in the context of linear algebra
Algebraic structure Scalar (physics) Linear algebra Matrix (mathematics) Row and column vectors Tensor Vector (mathematics and physics) Vector calculus Lay,
Scalar_(mathematics)
Stochastic matrix representing links between entities
Assuming there are N pages, we can fill out A by doing the following: A matrix element A i , j {\displaystyle A_{i,j}} is filled with 1 if node j {\displaystyle
Google_matrix
Ray tracing technique
paraxial rays. Each optical element (surface, interface, mirror, or beam travel) is described by a 2 × 2 ray transfer matrix which operates on a vector
Ray_transfer_matrix_analysis
Matrices important in quantum mechanics and the study of spin
of the Pauli matrices, see Spin (physics) § Higher spins Exchange matrix (the first Pauli matrix is an exchange matrix of order two) Split-quaternion This
Pauli_matrices
Algebraic object with geometric applications
high-dimensional matrix. Tensors have become important in physics, because they provide a concise mathematical framework for formulating and solving physics problems
Tensor
Group that is also a differentiable manifold with group operations that are smooth
widely used in many parts of modern mathematics and physics. Lie groups were first found by studying matrix subgroups G {\displaystyle G} contained in GL n
Lie_group
Matrix relating a system's generalized coordinate vector and kinetic energy
In analytical mechanics, the mass matrix is a symmetric matrix M that expresses the connection between the time derivative q ˙ {\displaystyle \mathbf {\dot
Mass_matrix
System for describing optical polarization
an optical element the resulting polarization of the emerging light is found by taking the product of the Jones matrix of the optical element and the Jones
Jones_calculus
Scientific subjects
physics, and molecular physics; optics and acoustics; condensed matter physics; high-energy particle physics and nuclear physics; and chaos theory and
Branches_of_physics
Branch of physics
banded matrix inversion to calculate the weights of basis functions (when modeled by finite element methods); matrix products (when using transfer matrix methods);
Computational electromagnetics
Computational_electromagnetics
Specialized notation for multivariable calculus
tensor index notation is preferred in physics. Two competing notational conventions split the field of matrix calculus into two separate groups. The
Matrix_calculus
Complex matrix A* obtained from a matrix A by transposing it and conjugating each entry
{\displaystyle ij} denotes the ( i , j ) {\displaystyle (i,j)} -th entry (matrix element), for 1 ≤ i ≤ n {\displaystyle 1\leq i\leq n} and 1 ≤ j ≤ m {\displaystyle
Conjugate_transpose
Random matrix with gaussian entries
distribution. They are among the most-commonly studied matrix ensembles, fundamental to both mathematics and physics. The three main examples are the Gaussian orthogonal
Gaussian_ensemble
Element in a ring whose some power is 0
In mathematics, an element x {\displaystyle x} of a ring R {\displaystyle R} is called nilpotent if there exists some positive integer n {\displaystyle
Nilpotent
Mathematical operation on vectors in 3D space
cross points to in the right-hand matrix. We then subtract the next element down on the left, multiplied by the element that the cross points to here as
Cross_product
Family of linear transformations
neighborhoods of the identity element of the Lie group. In the case of the Lorentz group, the exponential map is just the matrix exponential. Globally, the
Lorentz_transformation
Chemical element with atomic number 108 (Hs)
2016[update]. In nuclear physics, an element is called heavy if its atomic number is high; lead (element 82) is one example of such a heavy element. The term "superheavy
Hassium
Pulling force transmitted axially
purposes than tension. Stress is a 3x3 matrix called a tensor, and the σ 11 {\displaystyle \sigma _{11}} element of the stress tensor is tensile force
Tension_(physics)
Vector operation
two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. If the two
Outer_product
Pictorial representation of the behavior of subatomic particles
particles or fields. The transition amplitude is then given as the matrix element of the S-matrix between the initial and final states of the quantum system.
Feynman_diagram
Chemical element with atomic number 80 (Hg)
Mercury is a chemical element; it has symbol Hg and atomic number 80. It is commonly known as quicksilver. A heavy, silvery d-block element, mercury is the
Mercury_(element)
Determinant of a subsection of a square matrix
In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns
Minor_(linear_algebra)
Function approximating net physical effect
without including all of the underlying physics, but instead, providing the momentum dependence of suitable matrix elements. It is further measured experimentally
Form factor (quantum field theory)
Form_factor_(quantum_field_theory)
Computer graphics simulation of deformable objects
with scientific methods, particularly in the case of finite element simulations. Several physics engines currently provide software for soft-body simulation
Soft-body_dynamics
Physics model
the second spring slack. Gaussian network model Anisotropic Network Model Stiffness matrix Spring-mass system Laplacian matrix The Physics of Springs
Spring_system
Gamma matrices for arbitrary Clifford algebras
_{a}^{\textsf {T}}} where the element on the left is the abstract group element, and the one on the right is the literal matrix transpose. As before, the
Higher-dimensional gamma matrices
Higher-dimensional_gamma_matrices
Mathematics concept
In mathematics, a Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose
Hadamard_matrix
Quantum feature of condensed-matter systems
\mathbf {r} )=n(\mathbf {r} )} is the diagonal element describing the local density. The density matrix is normalized such that integrating over the volume
Off-diagonal_long-range_order
Chemical element with atomic number 20 (Ca)
Calcium is a chemical element; it has symbol Ca and atomic number 20. As an alkaline earth metal, calcium is a reactive metal that forms a dark oxide-nitride
Calcium
Chemical element with atomic number 74 (W)
Tungsten (also called wolfram) is a chemical element; it has symbol W (from German: Wolfram) and atomic number 74. It is a metal found naturally on Earth
Tungsten
Chemical element with atomic number 112 (Cn)
stability In nuclear physics, an element is called heavy if its atomic number is high; lead (element 82) is one example of such a heavy element. The term "superheavy
Copernicium
matrix of size q + 1. Here j is the all-1 column vector of length q and I is the (q+1)×(q+1) identity matrix. The matrix H is a skew Hadamard matrix,
Paley_construction
Nonassociative algebra over the real numbers
vectors using a modified version of matrix multiplication. Specifically, define a vector-matrix to be a 2×2 matrix of the form [ a v w b ] , {\displaystyle
Split-octonion
Type of group in mathematics
of determinant 1, and therefore not an element of the component. By extension, for any field F, an n × n matrix with entries in F such that its inverse
Orthogonal_group
Requirement that quantum states' time evolution operators are unitary transformations
imaginary part of the S-matrix. In order to see what the right-hand side is, let us look at any specific element of this matrix, e.g. between some initial
Unitarity
Type of geometric transformation
if S is a shear matrix with shear element λ, then Sn is a shear matrix whose shear element is simply nλ. Hence, raising a shear matrix to a power n multiplies
Shear_mapping
Partial order on matrices
functions. These functions arise naturally in matrix and operator theory and have applications in many areas of physics and engineering. Let A and B be two Hermitian
Loewner_order
Idealization of a large number of atomic-sized systems
the observables to their expectation values. Density matrix – Mathematical tool in quantum physics Ensemble (fluid mechanics) – Imaginary collection of
Ensemble (mathematical physics)
Ensemble_(mathematical_physics)
In mathematics, invariant of square matrices
square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the
Determinant
Soviet theoretical physicist (1908–1968)
in plasma physics, the Landau pole in quantum electrodynamics, the two-component theory of neutrinos, and Landau's equations for S-matrix singularities
Lev_Landau
Method for approximating eigenvalues
finite element method, the matrix H k j {\displaystyle H_{kj}} is precisely the stiffness matrix of the Hamiltonian in the piecewise linear element space
Rayleigh–Ritz_method
Electron-positron scattering
the scattering and annihilation diagrams contribute to the transition matrix element. By letting k and k' represent the four-momentum of the positron, while
Bhabha_scattering
Planar movement within a Euclidean space without rotation
remaining unchanged. In all translations, it is observed that the same element moves in a certain direction and always parallel to itself, that is, without
Translation_(geometry)
element of G can be uniquely decomposed as the product of an element of N and an element of H. (Unlike for the direct product of groups, the element of
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Symmetry of spatially mirrored systems
in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions. A matrix representation of P (in any
Parity_(physics)
Algebraic element satisfying some of the criteria of an inverse
them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class
Generalized_inverse
Coordinate change in linear algebra
a vector space of finite dimension n allows representing uniquely any element of the vector space by a coordinate vector, which is a finite sequence
Change_of_basis
Function acting on the space of physical states in physics
\phi _{i}\left|{\hat {A}}\right|\phi _{j}\right\rangle ,} which is a matrix element: A ^ = ( A 11 A 12 ⋯ A 1 n A 21 A 22 ⋯ A 2 n ⋮ ⋮ ⋱ ⋮ A n 1 A n 2 ⋯ A
Operator_(physics)
Irreducible representation of the rotation group SO
=D_{m'm}^{j}(0,\beta ,0)} is an element of the orthogonal Wigner's (small) d-matrix (sometimes referred to as the reduced Wigner D-matrix). That is, in this basis
Wigner_D-matrix
This glossary of physics is a list of definitions of terms and concepts relevant to physics, its sub-disciplines, and related fields, including mechanics
Glossary_of_physics
This is a list of notable software packages that implement the finite element method for solving partial differential equations. This table is contributed
List of finite element software packages
List_of_finite_element_software_packages
Numerical simulations of physical problems via computers
Computational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first
Computational_physics
Mathematical operation in quantum optics, general relativity and other areas of physics
Gennes matrix. Also in nuclear physics, this method is applicable, since it may describe the "pairing energy" of nucleons in a heavy element. The Hilbert
Bogoliubov_transformation
Ability of a body to store an electrical charge
capacitance matrix is singular (it has a 0 eigenvalue due to charge neutrality), and so formally the elastance matrix as the inverse of the capacitance matrix is
Capacitance
Mathematical operation on matrices
block matrix. It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the
Kronecker_product
Numerical integration scheme for Hamiltonian systems
dynamics, molecular dynamics, discrete element methods, accelerator physics, plasma physics, quantum physics, and celestial mechanics. Symplectic integrators
Symplectic_integrator
Vector formula for a rotation in space, given its axis
the rotation matrix through an angle θ counterclockwise about the axis k, and I the 3 × 3 identity matrix. This matrix R is an element of the rotation
Rodrigues'_rotation_formula
Theory of subatomic structure
the theory is known. In mathematics, a matrix is a rectangular array of numbers or other data. In physics, a matrix model is a particular kind of physical
String_theory
Concept in linear algebra
A quaternionic matrix is a matrix whose elements are quaternions. The quaternions form a noncommutative ring, and therefore addition and multiplication
Quaternionic_matrix
Transition rate formula
initial and final states of the system (described by the square of the matrix element of the perturbation) as well as the density of states. It is also applicable
Fermi's_golden_rule
Chemical element with atomic number 100 (Fm)
the case. A group at the Nobel Institute for Physics in Stockholm independently discovered the element, producing an isotope later confirmed to be 250Fm
Fermium
Type of group and algebra representation
translated into matrix multiplication of the representations: D ( a b ) = D ( a ) D ( b ) {\displaystyle D(ab)=D(a)D(b)} If e is the identity element of the group
Irreducible_representation
Algebra associated to any vector space
coefficient in this last expression is precisely the determinant of the matrix [v w]. The fact that this may be positive or negative has the intuitive
Exterior_algebra
German physicist (1901–1976)
scattering matrix, or S-matrix, in elementary particle physics. The first two papers were published in 1943 and the third in 1944. The S-matrix described
Werner_Heisenberg
Vector space equipped with a bilinear product
identity element with respect to the multiplication. The ring of real square matrices of order n forms a unital algebra since the identity matrix of order
Algebra_over_a_field
Manner of referring to elements of arrays or tensors
different methods for referring to the elements of a list, a vector, or a matrix, depending on whether one is writing a formal mathematical paper for publication
Index_notation
Geometric object that has length and direction
This matrix equation relates the scalar components of a in the n basis (u,v, and w) with those in the e basis (p, q, and r). Each matrix element cjk is
Euclidean_vector
Concept in differential geometry
{\displaystyle {e^{i}}_{j}} is the matrix with 1 at the (i, j)-th entry and zero on the other entries. The matrix F i j {\displaystyle {F^{i}}_{j}} whose
Exterior_covariant_derivative
Mathematical entity to describe the probability of each possible measurement on a system
Density matrix theory and applications, page 39. The concept of quantum states, in particular the content of the section Formalism in quantum physics above
Quantum_state
&&\\&&&&&0&1\\&&&&&-1&0\end{array}}\right)~.} Each element of a circular ensemble is a unitary matrix, so it has eigenvalues on the unit circle: λ k = e
Circular_ensemble
matrix calculations, combined with extensive Html reporting. Euler Mathematical Toolbox is an open-source numerical software system combining matrix language
List of open-source software for mathematics
List_of_open-source_software_for_mathematics
MATRIX ELEMENT-PHYSICS
MATRIX ELEMENT-PHYSICS
Male
English
Pet form of English Martin, MARTIE means "of/like Mars."
Female
English
Pet form of English Matilda, MATTIE means "mighty in battle." Compare with masculine Mattie.
Surname or Lastname
English
English : patronymic from the personal name Clement.German, Dutch, and Danish : from the personal name Clemens (see Clement).Samuel Langhorne Clemens, better known by his pen name, Mark Twain, was descended from VA stock on his father’s side, from a Robert Clemens, who was born in Warwickshire, England, in 1634.
Female
Finnish
Finnish form of Greek Maria, MAARIA means "obstinacy, rebelliousness" or "their rebellion."Â
Male
French
 French form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Male
English
 English form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Male
English
English surname transferred to forename use, derived from Latin Clemens or Clement, CLEMENTS means "gentle and merciful."
Female
English
English form of Latin Viatrix, BEATRIX means "voyager (through life)."
Male
English
Pet form of English Matthew, MATTIE means "gift of God." Compare with feminine Mattie.
Female
German
Pet form of German Katarine, KATRIN means "pure."
Female
Welsh
Welsh form of Old French Caterine, CATRIN means "pure."
Boy/Male
English American Danish
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Boy/Male
English American Biblical Latin
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Female
English
French form of Latin Maria, MARIE means "obstinacy, rebelliousness" or "their rebellion."
Female
Finnish
Finnish form of Greek Margarites, MAARIT means "pearl."
Boy/Male
Australian, British, Danish, Dutch, English, Finnish, French, German, Irish, Latin, Swedish
Gentle; Merciful; Mild; Form of Clement
Surname or Lastname
English, French, and Dutch
English, French, and Dutch : from the Latin personal name Clemens meaning ‘merciful’ (genitive Clementis). This achieved popularity firstly through having been borne by an early saint who was a disciple of St. Paul, and later because it was selected as a symbolic name by a number of early popes. There has also been some confusion with the personal name Clemence (Latin Clementia, meaning ‘mercy’, an abstract noun derived from the adjective; in part a masculine name from Latin Clementius, a later derivative of Clemens). As an American family name, Clement has absorbed cognates in other continental European languages. (For forms, see Hanks and Hodges 1988.)
Girl/Female
Arabic, Australian, Basque, French, Latin
Lady; Feminine of Martin; Warlike
Male
English
Short form of Latin Clementius, CLEMENT means "gentle and merciful." meaning "gentle and merciful." In the bible, this is the name of a companion of Paul.
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
MATRIX ELEMENT-PHYSICS
MATRIX ELEMENT-PHYSICS
Surname or Lastname
English (Bedfordshire)
English (Bedfordshire) : variant of Pipkin.The Pitkin name was introduced by William Pitkin, a leading lawyer and judge in CT, who migrated from Marylebone, London, to Hartford, CT, in 1660. William was probably the largest landowner on the east side of the Connecticut River, where he owned part of a saw and grist mill.
Boy/Male
Greek English
Farmer.
Girl/Female
Greek Latin American
Christian.
Girl/Female
Tamil
Saraswathi | ஸரஸà¯à®µà®¾à®¤à¯€Â
Goddess Saraswati, Tamil Goddess for education, Goddess of learning
Girl/Female
Arabic, Australian
Happiness; Good Fortune; Happy
Surname or Lastname
English (Durham)
English (Durham) : habitational name from Brantingham in East Yorkshire, named in Old English as ‘the homestead (hÄm) of the people of Branta’, or possibly as ‘homestead of the people living on a hillside’, from Old English brant ‘hillside’, ‘steep slope’.
Girl/Female
Hindu, Indian
Aspire
Girl/Female
Hindu, Indian
Gift
Girl/Female
Arabic, Muslim
Spirituality
Girl/Female
French American
The French form of the Latin Diana. Famous bearer: Diane de Poitiers, mistress of France's King...
MATRIX ELEMENT-PHYSICS
MATRIX ELEMENT-PHYSICS
MATRIX ELEMENT-PHYSICS
MATRIX ELEMENT-PHYSICS
MATRIX ELEMENT-PHYSICS
n.
The four elements were, air, earth, water, and fire
n.
Sometimes a curve, or surface, or volume is considered as described by a moving point, or curve, or surface, the latter being at any instant called an element of the former.
pl.
of Matrix
a.
Acting with great force; furious; violent; impetuous; forcible; mighty; as, vehement wind; a vehement torrent; a vehement fire or heat.
pl.
of Maori
n.
The quotient of a unit divided by eleven; one of eleven equal parts.
n.
The elements of the alchemists were salt, sulphur, and mercury.
n.
The simplest or fundamental principles of any system in philosophy, science, or art; rudiments; as, the elements of geometry, or of music.
a.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
n.
Any outline or sketch, regarded as containing the fundamental ideas or features of the thing in question; as, the elements of a plan.
v. t.
To constitute; to make up with elements.
v. t.
To compound of elements or first principles.
n.
One of the necessary data or values upon which a system of calculations depends, or general conclusions are based; as, the elements of a planet's orbit.
a.
Constituting one of eleven parts into which a thing is divided; as, the eleventh part of a thing.
n.
One out of several parts combined in a system of aggregation, when each is of the nature of the whole; as, a single cell is an element of the honeycomb.
n.
An infinitesimal part of anything of the same nature as the entire magnitude considered; as, in a solid an element may be the infinitesimal portion between any two planes that are separated an indefinitely small distance. In the calculus, element is sometimes used as synonymous with differential.
n.
One of the ultimate parts which are variously combined in anything; as, letters are the elements of written language; hence, also, a simple portion of that which is complex, as a shaft, lever, wheel, or any simple part in a machine; one of the essential ingredients of any mixture; a constituent part; as, quartz, feldspar, and mica are the elements of granite.
n.
See Matrix.
a.
Of or pertaining to the Maoris or to their language.