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Topics referred to by the same term
Look up multilinear in Wiktionary, the free dictionary. Multilinear may refer to: Multilinear form, a type of mathematical function from a vector space
Multilinear
Algebraic object with geometric applications
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space
Tensor
Vector-valued function of multiple vectors, linear in each argument
linear algebra, a multilinear map is a function of several variables that is linear separately in each variable. More precisely, a multilinear map is a function
Multilinear_map
Multilinear map that is 0 whenever arguments are linearly dependent
In mathematics, more specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments belonging to the same
Alternating_multilinear_map
Branch of mathematics
Multilinear algebra is the study of functions with multiple vector-valued arguments, with the functions being linear maps with respect to each argument
Multilinear_algebra
Type of polynomial
In algebra, a multilinear polynomial is a multivariate polynomial that is linear (meaning affine) in each of its variables separately, but not necessarily
Multilinear_polynomial
Map from multiple vectors to an underlying field of scalars, linear in each argument
In abstract algebra and multilinear algebra, a multilinear form on a vector space V {\displaystyle V} over a field K {\displaystyle K} is a map f : V k
Multilinear_form
Approach to dimensionality reduction
Multilinear subspace learning is an approach for disentangling the causal factor of data formation and performing dimensionality reduction. The Dimensionality
Multilinear_subspace_learning
Multilinear extension of principal component analysis
Multilinear principal component analysis (MPCA) is a multilinear extension of principal component analysis (PCA) that is used to analyze M-way arrays,
Multilinear principal component analysis
Multilinear_principal_component_analysis
Multilinear filmmaking style
Hyperlink cinema is a style of filmmaking characterized by complex or multilinear narrative structures with multiple characters under one unifying theme
Hyperlink_cinema
In multilinear algebra, applying a map that is the tensor product of linear maps to a tensor is called a multilinear multiplication. Let F {\displaystyle
Multilinear_multiplication
Gameplay involving unordered sequences
A video game with nonlinear gameplay presents players with challenges that can be completed in a number of different sequences. Each may take on (or even
Nonlinear_gameplay
Concept in machine learning
refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional
Tensor_(machine_learning)
Coordinate-free definition of a tensor
views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear
Tensor_(intrinsic_definition)
Vector behavior under coordinate changes
In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Australian and American mathematician (born 1975)
[T04b] With Camil Muscalu and Christoph Thiele, Tao considered certain multilinear singular integral operators with the multiplier allowed to degenerate
Terence_Tao
Property of math operations which yield an inverse result when arguments' order reversed
symmetry is of central importance, or even just in multilinear algebra these operations are mostly (multilinear with respect to some vector structures and then)
Anticommutative_property
Mathematical operation
\Phi (v_{s})),} which is a multilinear form on V. Hence Φ∗ is a (linear) operator from multilinear forms on W to multilinear forms on V. As a special case
Pullback (differential geometry)
Pullback_(differential_geometry)
2026 video game
5, Windows, and Xbox Series X/S on 12 May. Directive 8020 features a multilinear plot in which decisions can significantly alter the trajectory of the
Directive_8020
Graphical notation for multilinear algebra calculations
tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions or tensors proposed by Roger Penrose in 1971. A diagram in
Penrose_graphical_notation
Mathematical study of invariants under symmetries
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of
Invariant_theory
lattice theory, denotes the meet or greatest lower bound operation. 3. In multilinear algebra, geometry, and multivariable calculus, denotes the exterior product
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Set-to-real map with diminishing returns
such that each 0 ≤ x i ≤ 1 {\displaystyle 0\leq x_{i}\leq 1} . Then the multilinear extension is defined as F ( x ) = ∑ S ⊆ Ω f ( S ) ∏ i ∈ S x i ∏ i ∉ S
Submodular_set_function
Algebra associated to any vector space
multilinear function f : V k → K {\displaystyle f\colon V^{k}\to K} is called an alternating multilinear form. The set of all alternating multilinear
Exterior_algebra
Topics referred to by the same term
structure that generalizes a linear subspace of a vector space Multilinear subspace in multilinear algebra, a subset of a tensor space that is closed under
Subspace
Evolutionary theory of social change
theorists were the first to introduce the idea of multilinear cultural evolution. Under multilinear theory, there are no fixed stages (as in unilinear
Cultural_evolution
Mathematical operation on vector spaces
they are seen as multilinear maps (see also tensors as multilinear maps). Thus the components of the tensor product of multilinear forms can be computed
Tensor_product
Determinant of a subsection of a square matrix
elements. A more systematic, algebraic treatment of minors is given in multilinear algebra, using the wedge product: the k-minors of a matrix are the entries
Minor_(linear_algebra)
American mathematician
was an American mathematician, known as a leading expert on linear and multilinear algebra. From 1944 to 1946, Marvin Marcus served in the United States
Marvin_Marcus
2000 video game
depending on the player's words and actions. Short describes this as "multilinear interactive fiction": while interactive fiction in general allows the
Galatea_(video_game)
Mathematical operation on vectors in 3D space
which are axiomatized as binary products satisfying the axioms of multilinearity, skew-symmetry, and the Jacobi identity. Many Lie algebras exist, and
Cross_product
A cryptographic n {\displaystyle n} -multilinear map is a kind of multilinear map, that is, a function e : G 1 × ⋯ × G n → G T {\displaystyle e:G_{1}\times
Cryptographic_multilinear_map
Tensor decomposition
In multilinear algebra, the higher-order singular value decomposition (HOSVD) is a misnomer. There does not exist a single tensor decomposition that retains
Higher-order singular value decomposition
Higher-order_singular_value_decomposition
Process of reducing the number of random variables under consideration
tensor representation can be used in dimensionality reduction through multilinear subspace learning. The main linear technique for dimensionality reduction
Dimensionality_reduction
Topics referred to by the same term
the free dictionary. A tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space
Tensor_(disambiguation)
Expression that may be integrated over a region
universal property of exterior powers, this is equivalently an alternating multilinear map: β p : ⨁ n = 1 k T p M → R . {\displaystyle \beta _{p}\colon \bigoplus
Differential_form
Mathematics formula
F:M_{n}(\mathbb {K} )\rightarrow \mathbb {K} } which is alternating multilinear with respect to columns and such that F ( I ) = 1 {\displaystyle F(I)=1}
Leibniz formula for determinants
Leibniz_formula_for_determinants
Branch of mathematics
manifolds. It uses the techniques of vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry
Differential_geometry
Social theory
provided the context for new theories such as cultural relativism and multilinear evolution, which criticizes the generalization of culture and hypothetical
Multilineal_evolution
Process in algebra
In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" (M-way array) as a sequence of elementary operations acting
Tensor_decomposition
Tensor in differential geometry
for each point p ∈ M {\displaystyle p\in M} , it gives rise to a (multilinear) map: R p : T p M × T p M × T p M → T p M . {\displaystyle \operatorname
Ricci_curvature
group Orientation (geometry) Improper rotation Symplectic structure Multilinear algebra Tensor Classical treatment of tensors Component-free treatment
Outline_of_linear_algebra
Sequence of operations for a task
Operator algebra Operator theory Harmonic analysis Fourier analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior
Algorithm
Motion of a certain space that preserves at least one point
(quaternions), and other algebraic things: see the section Linear and Multilinear Algebra Formalism for details. A general rotation in four dimensions
Rotation_(mathematics)
Topics referred to by the same term
Yosemite Airport. IATA code Mackay Memorial Hospital, Taipei, Taiwan Multilinear Modular Hashing, a computer algorithm Manual material handling Mark McHugh
MMH
Topics referred to by the same term
definiteness, a concept in quantum mechanics For the definiteness of forms in multilinear algebra, see Definite quadratic form. Definition (disambiguation) Definitive
Definiteness_(disambiguation)
Subset of artificial intelligence
representation is sparse, meaning that the mathematical model has many zeros. Multilinear subspace learning algorithms aim to learn low-dimensional representations
Machine_learning
Mathematical Theorem
Gamas's theorem is a result in multilinear algebra which states the necessary and sufficient conditions for a tensor symmetrized by an irreducible representation
Gamas's_theorem
Choice of reference for distinguishing an object and its mirror image
The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented
Orientation_(vector_space)
Matrix operation which flips a matrix over its diagonal
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Transpose
Function of two vectors linear in each argument
ring R. It generalizes to n-ary functions, where the proper term is multilinear. For non-commutative rings R and S, a left R-module M and a right S-module
Bilinear_map
2021 video game
is the third game of The Dark Pictures Anthology. The game features a multilinear plot in which decisions can significantly alter the trajectory of the
The Dark Pictures Anthology: House of Ashes
The_Dark_Pictures_Anthology:_House_of_Ashes
Technique for expressing a polynomial in simpler fashion by using more variables
given a homogeneous polynomial, polarization produces a unique symmetric multilinear form from which the original polynomial can be recovered by evaluating
Polarization of an algebraic form
Polarization_of_an_algebraic_form
Algorithm for reducing the dimension of tensors
In statistics, machine learning and algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors
Tensor_sketch
Algorithms for matrix decomposition
rational. Recently, this problem has been answered negatively. Multilinear algebra Multilinear subspace learning Tensor Tensor decomposition Tensor software
Non-negative matrix factorization
Non-negative_matrix_factorization
Algebraic structure
space. Let S q ( V ) {\displaystyle S^{q}(V)} denote the vector space of multilinear functionals λ : ∏ 1 q V → k {\displaystyle \textstyle \lambda :\prod
Ring_of_polynomial_functions
Branch of mathematics
Commutative Elementary Field theory Group theory Homological Lie Linear Multilinear Ring theory Universal Analysis Calculus Real analysis Complex analysis
Abstract_algebra
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Kronecker_delta
Topological space that locally resembles Euclidean space
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Manifold
associated statistics are called U-statistics. Alternating multilinear map – Multilinear map that is 0 whenever arguments are linearly dependent Antisymmetric
Symmetrization
Concept in multilinear algebra and representation theory
In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor A {\displaystyle \mathbf
Invariants_of_tensors
Type of cryptographic software obfuscation
construction of iO based on a computational hardness assumption relating to multilinear maps, but this assumption was later disproven. A construction based on
Indistinguishability obfuscation
Indistinguishability_obfuscation
Array of numbers describing a metric connection
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Christoffel_symbols
Isomorphism between the tangent and cotangent bundles of a manifold
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Musical_isomorphism
Continuous surjection satisfying a local triviality condition
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Fiber_bundle
engineering science For some history of the abstract theory see also multilinear algebra. Ricci calculus The earliest foundation of tensor theory – tensor
Glossary_of_tensor_theory
Differential form of degree one or section of a cotangent bundle
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
One-form
American applied mathematician
Laboratories. She is noted for her contributions in computational science, multilinear algebra, data mining, graph algorithms, mathematical optimization, parallel
Tamara_G._Kolda
Polish American mathematician
Institutions Yale University UCD Thesis Invariants of Links and 3-Manifolds via Multilinear Algebra and Hopf Algebras (1991) Doctoral advisor Andrew Casson
Greg_Kuperberg
2020 video game
player to see visions of possible future events. The game features a multilinear plot in which decisions can alter the trajectory of the story and change
The Dark Pictures Anthology: Little Hope
The_Dark_Pictures_Anthology:_Little_Hope
Exterior algebraic map taking tensors from p forms to n-p forms
{\displaystyle {\textstyle \bigwedge }^{\!n}V^{*}} of n-forms (alternating n-multilinear functions on V n {\displaystyle V^{n}} ), the dual to ω {\displaystyle
Hodge_star_operator
Commutative Elementary Field theory Group theory Homological Lie Linear Multilinear Ring theory Universal Analysis Calculus Real analysis Complex analysis
Numerical_algebraic_geometry
German polymath, linguist and mathematician (1809–1877)
Grassmann awaited the concept of vector spaces, which then could express the multilinear algebra of his extension theory. To establish the priority of Grassmann
Hermann_Grassmann
Assignment of a tensor continuously varying across a region of space
tensor fields!) on M as multilinear maps on vectors and covectors, we can regard general (k,l) tensor fields on M as C∞(M)-multilinear maps defined on k copies
Tensor_field
Set of vectors used to define coordinates
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Basis_(linear_algebra)
Complex matrix whose conjugate transpose equals its inverse
Edward (2002). "Additive decomposition of real matrices". Linear and Multilinear Algebra. 50 (4): 321–326. doi:10.1080/03081080290025507. S2CID 120125694
Unitary_matrix
Greek mathematician
Calderón–Zygmund theory. He is well known for his contributions to the area of multilinear harmonic analysis. Grafakos has been supported by the National Science
Loukas_Grafakos
Concept of social inter-connectedness
with mathematician Paul Erdős and actor Kevin Bacon Hyperlink cinema – Multilinear filmmaking style Jewish geography – Game amongst global Jewish community
Six_degrees_of_separation
Specification of a derivative along a tangent vector of a manifold
be a tensor field of type (p, q). Consider T to be a differentiable multilinear map of smooth sections α1, α2, ..., αq of the cotangent bundle T∗M and
Covariant_derivative
Norm on a vector space of matrices
"A characterization of certain classes of matrix norms". Linear and Multilinear Algebra. 13 (2): 97–99. doi:10.1080/03081088308817508. ISSN 0308-1087
Matrix_norm
Message authentication code
and "Fin." denotes finalization with IV-setup. The name MMH stands for Multilinear-Modular-Hashing. Applications in Multimedia are for example to verify
MMH-Badger_MAC
Mathematical object that describes the electromagnetic field in spacetime
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Electromagnetic_tensor
Algebra with a graded anticommutativity property on multiplication
ring R in which 2 is not a zero divisor is alternating. Alternating multilinear map Exterior algebra Graded-symmetric algebra Supercommutative algebra
Alternating_algebra
In mathematics, invariant of square matrices
value of the determinant. This is a consequence of multilinearity and being alternative: by multilinearity the determinant changes by a multiple of the determinant
Determinant
Topics referred to by the same term
link Alternating map, a multilinear map that is zero whenever any two of its arguments are equal Alternating operator, a multilinear map in algebra Alternating
Alternating
British mathematician
the London Mathematical Society in 2011 for "his foundational work on multilinear inequalities in harmonic and geometric analysis, and for a number of
Jonathan Bennett (mathematician)
Jonathan_Bennett_(mathematician)
Spatial statistical signal analysis
kernel trick for more information). Blind signal separation Multilinear PCA Multilinear subspace learning Nonlinear dimensionality reduction Orthogonal
Empirical orthogonal functions
Empirical_orthogonal_functions
Method of data analysis
associated with a positive definite kernel. In multilinear subspace learning, PCA is generalized to multilinear PCA (MPCA) that extracts features directly
Principal_component_analysis
Method for specifying point positions
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Coordinate_system
System of moving vectors in differential geometry
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Parallel_transport
Automated recognition of patterns and regularities in data
mixture of experts Bayesian networks Markov random fields Unsupervised: Multilinear principal component analysis (MPCA) Kalman filters Particle filters Gaussian
Pattern_recognition
Mathematical operation on matrices
Shayle R. (1983). "On the history of the kronecker product". Linear and Multilinear Algebra. 14 (2): 113–120. doi:10.1080/03081088308817548. hdl:1813/32834
Kronecker_product
Second order tensor in vector algebra
In mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra
Dyadics
Classification scheme for mathematics
(Commutative rings and algebras) 14: Algebraic geometry 15: Linear and multilinear algebra; matrix theory 16: Associative rings and (associative) algebras
Mathematics Subject Classification
Mathematics_Subject_Classification
Tensor field in Riemannian geometry
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Riemann_curvature_tensor
Shorthand notation for tensor operations
Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision
Einstein_notation
Study of abstract machines and automata
Operator algebra Operator theory Harmonic analysis Fourier analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior
Automata_theory
Topics referred to by the same term
Differential form, a concept from differential topology that combines multilinear forms and smooth functions First-order reliability method, a semi-probabilistic
Form
Concept in algebra
definition is a discriminant for a singular point on a scalar valued multilinear map. Cayley's first hyperdeterminant is defined only for hypercubes having
Hyperdeterminant
(film and video production) – Filmmaking technique Hyperlink cinema – Multilinear filmmaking style British Pathe The birth of A Place to Stand, Christopher
Multi-dynamic_image_technique
MULTILINEAR
MULTILINEAR
MULTILINEAR
MULTILINEAR
Girl/Female
Tamil
Victory, Goddess Parvati
Biblical
wandering
Girl/Female
Muslim
Young and delicate, Soft
Surname or Lastname
English
English : patronymic from the personal name Robin.
Girl/Female
English American Italian Latin
Legendary princess.
Girl/Female
Muslim
Adorning the world daughter, Queen of the world
Male
English
 Anglicized form of Greek Ioannes (Latin Johannes), JOHN means "God is gracious." In the bible, this is the name of many characters, including John the Baptist.
Boy/Male
Hindu
Female
Hindi/Indian
(शोà¤à¤¾) Hindi name SHOBHA means "brilliance."
Girl/Female
Irish Italian Greek Swedish
Kind.
MULTILINEAR
MULTILINEAR
MULTILINEAR
MULTILINEAR
MULTILINEAR