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Infinite Quasi-Normal Matrices

Published online by Cambridge University Press:  20 November 2018

N. A. Wiegmann
N. A. Wiegmann*
Affiliation:
California State College at Dominguez Hills, Dorninguez Hills, California
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If A is a finite matrix with complex elements, and if A = AT (where AT denotes the transpose of A ), it is known (see [8] ) that there exists a unitary matrix U such that UA UT = D is a real diagonal matrix with non-negative elements which is a canonical form for A relative to the given U, UT transformation.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 820 - 828
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bellman, R., Introduction to matrix analysis (McGraw-Hill, New York, 1960).Google Scholar
2. Berberian, S., Introduction to Hilbert space (Oxford University Press, Oxford, 1961).Google Scholar
3. Gelfand, and Vilenkin, , Generalized functions (Academic Press, New York, 1964).Google Scholar
4. Halmos, P., A Hilbert space problem book (Van Nostrand, Princeton, 1967).Google Scholar
5. Stone, M., Linear transformation in Hilbert space (Amer. Math. Soc. Colloquim Publication, New York, 1932).Google Scholar
6. Morita, K., Über normale antilineare Transformationen, Proc. Japan Acad. 20 (1944), 715–726.Google Scholar
7. Schatten, R., Norm ideals of completely continuous operators (Springer-Verlag, New York, 1960).Google Scholar
8. Schur, I., Ein Satz über quadratische Formen mit komplexen koeffizienten, Amer. J. Math. 67 (1945), 472–480.Google Scholar
9. Stander, and Wiegmann, , Canonical forms for certain matrices under unitary congruence, Can. J. Math. 12 (1960), 438–446.Google Scholar
10. Wiegmann, N. A., Quasi-normal matrices and Products, J. Austral. Math. Soc. 11 (1970), 329–339.Google Scholar