# Kronecker product

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## Kronecker product

[′krō·nek·ər ‚präd·əkt]
(mathematics)
Given two different representations of the same group, their Kronecker product is a representation of the group constructed by taking direct products of matrices from the respective representations.
References in periodicals archive ?
The array aperture is greatly expanded by the vectorization method and the Kronecker product operation, and the array DOF is increased.
Operator [cross product] is the Kronecker product and [I.sub.L] is the L x L identity matrix.
A is the relationship matrix, I is an identity matrix, (Eq.) is the Kronecker product between matrices and R is a block diagonal matrix containing residual variances.
The superscrip[t.sup.T] denotes transposition, and [cross product] stands for the Kronecker product. We refer to [8, 15] for derivations of the global Lanczos decomposition (1.5).
[cross product] represents Kronecker product. For a given matrix or vector X, [X.sup.T], and [parallel]X[parallel] represent the transpose and European norm of X, respectively.
[(*).sup.T], [(*).sup.H], and [(*).sup.-1] denote transpose, conjugate-transpose, and inverse operations, respectively; [cross product] represents the Kronecker product; diag(v) stands for diagonal matrix whose diagonal element is a vector v; [I.sub.K] is a K x K identity matrix; Re(*) and Im(*) denotes the real part and imaginary part of a complex number, respectively.
Broxson, "The Kronecker Product," UNF, Theses and Dissertations, Paper 25, http://digitalcommons.unf.edu/etd/25, 2006.
A [cross product] B denotes the Kronecker product. E{x} denotes mathematical expectation; Pr{[alpha]} represents the probability of an event [alpha].
G and P are the (co)variance of additive genetic and permanent environment effects, A is the relationship matrix, R = I [[sigma].sup.2.sub.e] is the diagonal matrix (residual) and [cross product] is Kronecker product between matrices.
Where [bar.[PSI]] = [bar.[PSI]] [producto cruzado]I, I is a [N.sup.2] X [N.sup.2] identity matrix and [producto cruzado] is the Kronecker product operator.
By exploiting the relation vec(ASD) = ([D.sup.T] [cross product] A)vec (S), where [cross product] denotes Kronecker product, we have
where [cross product] is the Kronecker product [[eta].sub.1] and, [[eta].sub.2], [[eta].sub.3], [[eta].sub.4], [r.sub.0] are arbitrary constants.
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