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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 |

### Keywords:

Kronecker product; mixed matrix products; vector operator; vec-permutation matrix; singular values; determinant; trace; rank; polynomial matrix### Software:

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\textit{H. Zhang} and \textit{F. Ding}, J. Appl. Math. 2013, Article ID 296185, 8 p. (2013; Zbl 1275.15019)

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### References:

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