2012 | OriginalPaper | Buchkapitel
Eigenvalues Estimation of Block Kronecker Product of Positive Semidefinite Hermitian Matrices
verfasst von : Zhongpeng Yang, Hongbin Lü, Xiaoxia Feng, Meixiang Chen
Erschienen in: Recent Advances in Computer Science and Information Engineering
Verlag: Springer Berlin Heidelberg
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In 1911, L. Schur showed the overall estimation for all eigenvalues of Hadamard products of positive semidefinite Hermitianmatrices. In 1992,R. A. Horn and R.Mathias obtained an approach to a block generalization of Schur’s Basic Theorem [Roger A. Horn, Roy Mathias, Block-matrix generalizations of Schur’s basic theorems on Hadamard products, Linear Algebra and its Applications, 172 (1992), 337-346.]. In this paper, we estimate every eigenvalue of the block Kronecker products of positive semidefinite Hermitian matrices under the conditions given by R. A. Horn and R. Mathias, then it has generalized the Schur’s Basic Theorem.