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Remarks on theorems of Thompson and Freede

Published online by Cambridge University Press:  17 April 2009

A.R. Amir-Moéz  and
C.R. Perry
A.R. Amir-Moéz
Affiliation:
Texas Tech University, Lubbock, Texas, USA.
C.R. Perry
Affiliation:
Texas Tech University, Lubbock, Texas, USA.
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Abstract

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Let A be a hermitian transformation on an n-dimensional unitary space En, with proper values a1 ≥ … ≥ an. Let M be a proper subspace of En. Suppose b1 ≥ … ≥ bh are the proper values of A/M and c1 ≥ … ≥ ck are the proper values of . Let i1. < … < ir and j1 < … < jr be sequences of positive integers, with ir ≤ k and jr ≤ h. then

.

This is a special case of one of the Thompson-Freede theorems which is proved by use of certain invariants.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 2 , October 1971 , pp. 221 - 225
Copyright
Copyright © Australian Mathematical Society 1971

References

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[4]Thompson, Robert C. and Freede, Linda J., “Eigenvalues of partitioned hermitian matrices”, Bull. Austral. Math. Soc. 3 (1970), 23–37.CrossRefGoogle Scholar
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