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Kronecker product of special matrices. (Chinese. English summary) Zbl 1212.15023
Summary: Based on the well-known properties of the Kronecker product, some other properties of Kronecker products of some special matrices are discussed, such as normal, diagonal, Hermite, congruent, nonnegative, positive definite, semi-positive definite and M-matrices, etc. The singular value decomposition of the Kronecker product is given. Moreover, the operative properties of the exponential matrix function of the Kronecker product and the operative properties of the Kronecker power for productive matrices are also proved. Finally, the differential operation rules of the Kronecker product are also obtained.

15A23 Factorization of matrices
15A15 Determinants, permanents, traces, other special matrix functions
15B57 Hermitian, skew-Hermitian, and related matrices
15B48 Positive matrices and their generalizations; cones of matrices
15A18 Eigenvalues, singular values, and eigenvectors
15A16 Matrix exponential and similar functions of matrices