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On the Kronecker products and their applications. (English) Zbl 1275.15019

Summary: This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vec-permutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of the Kronecker products.

MSC:

15A69 Multilinear algebra, tensor calculus
15A18 Eigenvalues, singular values, and eigenvectors
15A15 Determinants, permanents, traces, other special matrix functions

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