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Extremal Properties Of Hermitian Matrices

Published online by Cambridge University Press:  20 November 2018

M. Marcus  and
J. L. McGregor
M. Marcus
Affiliation:
United States Naval Ordnance Test Station, California Institute Pasadena, University of British Columbia.
J. L. McGregor
Affiliation:
California Institute of Technology
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In (1) Fan showed that if A is a Hermitian matrix with eigenvalues λ1 ≤ … ≤ λn then, for k ≤ n,

,

,

where X1, … , xk run over all sets of k orthonormal (o.n.) vectors in unitary n-space V.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 524 - 531
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Fan, Ky, On a theorem of Weyl concerning eigenvalues of linear transformations I, Proc. N.A.S. (U.S.A.), 35 (1949), 652–655.Google Scholar
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6. Wedderburn, J. H. M., Lectures on matrices, Amer. Math. Soc. Colloq. Pub., 17 (1934)Google Scholar