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Some New Bounds for Singular Values and Eigenvalues of Matrix Products

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Abstract

For two Hermitian matrices A and B, at least one of which is positive semidefinite, we give upper and lower bounds for each eigenvalue of AB in terms of the eigenvalues of A and B. For two complex matrices A,B with known singular values, upper and lower bounds are deduced for each singular value of AB.

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Authors and Affiliations

  1. Department of Mathematics, Xiamen University, Xiamen, 361005, PR China

    L.-Z. Lu

  2. Department of Applied Mathematics, The University of Adelaide, Adelaide, SA 5005, Australia

    C.E.M. Pearce

Authors
  1. L.-Z. Lu
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  2. C.E.M. Pearce
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Lu, LZ., Pearce, C. Some New Bounds for Singular Values and Eigenvalues of Matrix Products. Annals of Operations Research 98, 141–148 (2000). https://doi.org/10.1023/A:1019200322441

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  • DOI: https://doi.org/10.1023/A:1019200322441

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