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Generalizing the inequality per(J2⊗M)⩾2n[per(M]2

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
102
Identifiers
DOI: 10.1016/0024-3795(88)90321-7

Abstract

Abstract Let M denote an n × n positive semidefinite Hermitian matrix,and let W = [ω ij ] be either a 2×2 real matrix such that ω 11ω 22⩽0 and ω 12ω 21⩽0 or a 2×2 Hermitian matrix such that ω 11ω 22⩽0. We prove the inequality per(W⊗M)⩾[ per(W)] n[ per(M)] 2 and establish that equality results if and only if ω 11ω 22 = 0 or ω 12ω 21=0 or M contains a row of zeros or M is diagonal.

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