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The determinant of the sum of two matrices

Published online by Cambridge University Press:  17 April 2009

Chi-Kwong Li
Affiliation:
Department of MathematicsCollege of William and MaryWilliamsburg VA 23187–8795United States of America, e-mail: ckli@cs.wm.edu, mathias@cs.wm.edu
Roy Mathias
Affiliation:
Department of MathematicsCollege of William and MaryWilliamsburg VA 23187–8795United States of America, e-mail: ckli@cs.wm.edu, mathias@cs.wm.edu
Corresponding
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Abstract

Let A and B be n × n matrices over the real or complex field. Lower and upper bounds for |det(A + B)| are given in terms of the singular values of A and B. Extension of our techniques to estimate |f(A + B)| for other scalar-valued functions f on matrices is also considered.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995

References

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[2]Bebiano, N., Li, C.K. and da Providencia, J., ‘Principal minors of the sum of a symmetric and a skew-symmetric matrix’, (preprint).Google Scholar
[3]Horn, R.A. and Johnson, C.R., Topics in matrix analysis (Cambridge Univsity Press, New York, 1991).CrossRefGoogle Scholar
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[7]Thompson, R.C. and Freede, L.J., ‘On the eigenvalues of sums of hermitian matrices’, Linear Algebra Appl. 4 (1971), 369376.CrossRefGoogle Scholar
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