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Kronecker product

In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a 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 tensor product linear map with respect to a standard choice of basis. The…

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Definition

Properties

Matrix equations

Related matrix operations

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Kronecker product

Nodes83
Edges82
Triples146
Avg. degree1.98
Density0.024096
Components1

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Kronecker product

Top relations

related to Relations to other matrix operations · 44
Kronecker product → Abstract, AC, As, BD, Bilinearity, Commutator, Determinant, F-linear, FinVectF, Furthermore, Hadamard, Hamiltonian, However, If, If Hr, Ik, In, Ir, It, Kron
related to References · 34
Kronecker product → Advanced Matrix Calculus, Anil, Applications, Bibcode, Cambridge University Press, Charles, Digital Image Processing, Fundamentals, Götz, Hadamard, Horn, Information, International Journal, Introductory, ISBN, Jain, Johnson, Khatri-Rao, Kronecker, Liu
related to External links · 20
Kronecker product → Archived, December, Direct Product, Earliest, EMS Press, Encyclopedia, Fortran, Kronecker, Mathematics, MathWorld, New Kronecker, PDF, PlanetMath, Retrieved, RosettaCode, Software, SourceForge, Tensor, The, Zehfuss
related to Abstract properties · 18
Kronecker product → Avi, Bwj, Cartesian, If, It, Kronecker, Let, Lie, Relation, Similarly, Since, Singular, Specifically, Spectrum, Suppose, The Kronecker, Then, When
has application · 11
Kronecker product → Another, Fast Walsh, FFT, For, Hadamard, Kronecker, Lyapunov, Splitting, SVD, This, To
related to Tracy–Singh product · 7
Kronecker product → Aij, Bkℓ, Essentially, Kronecker, Singh, The Tracy, Tracy
related to Matrix equations · 5
Kronecker product → AXB, Consider, Here, The Kronecker, We
related to Khatri–Rao product · 3
Kronecker product → Block Kronecker, Khatri, Rao
is a · 2
Kronecker product → representation of the tensor product in the chosen bases.Transpose, special case of the tensor product
related to Definition · 2
Kronecker product → If, Kronecker

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Important terminology

product kronecker matrix displaystyle matrices mathbf otimes two tensor property also called operatorname operation similarly identity size vectors mixed-product vec

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Kronecker productis aspecial case of the tensor product0.90text
Kronecker productis arepresentation of the tensor product in the chosen bases.Transpose0.90text
Kronecker producthas applicationFor0.60section
Kronecker producthas applicationLyapunov0.60section
Kronecker producthas applicationThis0.60section
Kronecker producthas applicationAnother0.60section
Kronecker producthas applicationKronecker0.60section
Kronecker producthas applicationFFT0.60section
Kronecker producthas applicationFast Walsh0.60section
Kronecker producthas applicationHadamard0.60section
Kronecker producthas applicationSplitting0.60section
Kronecker producthas applicationSVD0.60section

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