Infinite Quasi-Normal Matrices

Wiegmann, N. A.

Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 820-828

Résumé

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.

Détail

DOI : 10.4153/CJM-1973-084-6

Bibliographie

[1] 1. Bellman, R., Introduction to matrix analysis (McGraw-Hill, New York, 1960). Google Scholar

[2] 2. Berberian, S., Introduction to Hilbert space (Oxford University Press, Oxford, 1961). Google Scholar

[3] 3. Gelfand, and Vilenkin, , Generalized functions (Academic Press, New York, 1964). Google Scholar

[4] 4. Halmos, P., A Hilbert space problem book (Van Nostrand, Princeton, 1967). Google Scholar

[5] 5. Stone, M., Linear transformation in Hilbert space (Amer. Math. Soc. Colloquim Publication, New York, 1932). Google Scholar

[6] 6. Morita, K., Über normale antilineare Transformationen, Proc. Japan Acad. 20 (1944), 715–726. Google Scholar

[7] 7. Schatten, R., Norm ideals of completely continuous operators (Springer-Verlag, New York, 1960). Google Scholar

[8] 8. Schur, I., Ein Satz über quadratische Formen mit komplexen koeffizienten, Amer. J. Math. 67 (1945), 472–480. Google Scholar

[9] 9. Stander, and Wiegmann, , Canonical forms for certain matrices under unitary congruence, Can. J. Math. 12 (1960), 438–446. Google Scholar

[10] 10. Wiegmann, N. A., Quasi-normal matrices and Products, J. Austral. Math. Soc. 11 (1970), 329–339. Google Scholar