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Imbedding Conditions for Hermitian and Normal Matrices

Published online by Cambridge University Press:  20 November 2018

Ky Fan
Affiliation:
University of Notre Dame and American University
Gordon Pall
Affiliation:
Illinois Institute of Technology
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Let A, B be two square matrices with complex coefficients, of respective orders n and m, where nm. We shall say that B is imbeddable in A if there exists a unitary matrix U of order n such that U*AU contains B a s a principal submatrix. In other words, B is said to be imbeddable in A if there exists a matrix V of type n × m such that V*V = IW (= the identity matrix of order m) and V*AV = B.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Cauchy, A., Sur l'équation à Vaide de laquelle on détermine les inégalités séculaires des mouvements des planètes; Oeuvres complètes, Second Ser., IX, 174195.Google Scholar
2. Hamburger, H. L. and Grimshaw, M. E., Linear Transformations in n-dimensional Vector Space (Cambridge, 1951).Google Scholar
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