Du, Juan; Fan, Xiaotao; Feng, Sichen Kronecker product of special matrices. (Chinese. English summary) Zbl 1212.15023 J. Sichuan Norm. Univ., Nat. Sci. 32, No. 1, 56-59 (2009). 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. Cited in 1 Document MSC: 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 Keywords:direct product; Kronecker product; normal matrices, diagonal matrices, Hermite matrices, congruent matrices, nonnegative matrices, positive definite matrices, semi-positive definite matrices; M-matrices; singular value decomposition; exponential matrix function PDF BibTeX XML Cite \textit{J. Du} et al., J. Sichuan Norm. Univ., Nat. Sci. 32, No. 1, 56--59 (2009; Zbl 1212.15023)