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Generalization of "A Theorem Concerning the Rearrangements of Two Sets" NICHD

Author(s):
Kristof, Walter
Publication Year:
1969
Report Number:
RB-69-85
Source:
ETS Research Bulletin
Document Type:
Report
Page Count:
9
Subject/Key Words:
National Institute for Child Health and Human Development (NICHD), Mathematical Formulas, Matrices, Statistical Analysis

Abstract

The range of the function tr Zeta Gamma Zeta * Delta is determined when Gamma and Delta are real diagonal matrices and matrix Zeta with hermitian transpose Zeta* varies unrestrictedly over the group of unitary matrices. Two equivalent versions of the result are given. The real case (Zeta restricted to be real orthogonal) is considered separately. Further specialization of the matrix argument yields a "very simple, but important," theorem on rearrangements of two finite sets of real numbers. Two applications are appended by way of illustration.

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