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The Generalizations of Schur’s Theorems on The Block Kronecker Product of Hermitian Matrices

Zhixing Lin, Zhongpeng Yang, Xiaoxia Feng, Meixiang Chen


The Schur’s Basic Theorem, established in 1911, defines the global bounds for all eigenvalues of Hadamard products of positive semidefinite Hermitian matrices. R. A. Horn and R. Mathias give an approach to a block generalization of Schur’s Basic Theorem [L. A. A. 172(1992), 337-346]. In this paper, we estimate every eigenvalue of the block Kronecker products of two Hermitian matrices.


Hermitian matrix, bound of eigenvalue, Hadamard product, block Kronecker product.

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