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Extremal Properties of Hermitian Matrices. II

Published online by Cambridge University Press:  20 November 2018

M. Marcus ,
B. N. Moyls  and
R. Westwick
M. Marcus
Affiliation:
The University of British Columbia
B. N. Moyls
Affiliation:
The University of British Columbia
R. Westwick
Affiliation:
The University of British Columbia
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Let H be an n-square Hermitian matrix with eigenvalues h1 ≥ h2 ≥ . . . ≥ hn. Fan (2) showed that

1

k — 1,2, … , n, where the max and min are taken over all sets of k orthonormal (o.n.) vectors in unitary w-space Vn. Marcus and McGregor (3) have generalized this result in the case that H is non-negative Hermitian. For vectors X1, … , xr r ≤ n, in Vn, let X1 Λ X2 Λ … Λ xT denote the Grassmann exterior product of the xt; it is a vector in Vm,, where

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 379 - 382
Copyright
Copyright © Canadian Mathematical Society 1959

References

1. Courant, R. and Hilbert, D., Methods of mathematical physics, vol. 1 (New York, 1953).Google Scholar
2. Fan, Ky, On a theorem of Weyl concerning eigenvalues of linear transformations, I, Proc. N.A.S. (U.S.A.), 35 (1949), 652-5.Google Scholar
3. Marcus, M. and McGrregor, J. L., Extremal properties of Hermitian matrices, Can. J. Math., 8 (1956), 524-31.Google Scholar