Journal of East China Normal University(Natural Sc ›› 2014, Vol. 2014 ›› Issue (6): 35-38.doi: 10.3969/j.issn.1000-5641.2014.06.006

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A new proof of the generalized Craig-Sakamoto theorem

 DU  Cui-Zhen   

  1. School of Mathematical Sciences, Huaibei Normal University, Huaibei Anhui 235000, China
  • Online:2014-11-25 Published:2015-02-07

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

CLC Number: