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A Note on Normal Matrices

Published online by Cambridge University Press:  20 November 2018

Marvin Marcus  and
Nisar Khan
Marvin Marcus
Affiliation:
U. S. National Bureau of Standards, Washington, D. C. and Muslim University, Aligarh, India and University of British Columbia
Nisar Khan
Affiliation:
U. S. National Bureau of Standards, Washington, D. C. and Muslim University, Aligarh, India and University of British Columbia
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In 1954 A.J. Hoffman and O. Taussky [1] showed that if A is an n-square complex matrix with eigenvalues λ = (λ1, …, λn ) and P is a permutation matrix for which αA + βA* has eigenvalues for some αβ ≠ 0 then A is normal. Here is the conjugate vector of λ. As a companion result they also proved that if the eigenvalues of AA* are , i = 1, …, n then A is normal.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 4 , Issue 1 , January 1961 , pp. 23 - 27
Copyright
Copyright © Canadian Mathematical Society 1961

References

Hoffman, A.J. and Taussky, O., A characterization of normal matrices, J. Research, Nat. Bur. Standards 52 (1954), 17-19.Google Scholar