Journal of East China Normal University(Natural Science) >

2014 , Vol. 2014 >Issue 6: 35 - 38

DOI: https://doi.org/10.3969/j.issn.1000-5641.2014.06.006

Article

A new proof of the generalized Craig-Sakamoto theorem

  • DU Cui-Zhen
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  • School of Mathematical Sciences, Huaibei Normal University, Huaibei Anhui 235000, China

Online published: 2015-02-07

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Abstract

We gave a new proof of the generalized Craig-Sakamoto theorem, which asserts that two normal matrices A and B satisfy det(I − aA − bB) = det(I − aA)det(I − bB) for all complex numbers a and b if and only if AB = O.

Key words： eigenvalues; singular values; normal matrices; quadratic forms

Cite this article

DU Cui-Zhen . A new proof of the generalized Craig-Sakamoto theorem[J]. Journal of East China Normal University(Natural Science), 2014 , 2014(6) : 35 -38 . DOI: 10.3969/j.issn.1000-5641.2014.06.006

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