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Mean Value and Limit Theorems for Generalized Matrix Functions

Published online by Cambridge University Press:  20 November 2018

Paul J. Nikolai
Paul J. Nikolai*
Affiliation:
Aerospace Research Laboratories (OAR), Wright-Patterson Air Force Base, Ohio;
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Let A = [aij] denote an n-square matrix with entries in the field of complex numbers. Denote by H a subgroup of Sn, the symmetric group on the integers 1, …, n, and by a character of degree 1 on H. Then

is the generalized matrix function of A associated with H and x; e.g., if H = Sn and χ = 1, then the permanent function. If the sequences ω = (ω1, …, ωm) and ϒ = (ϒ1, …, ϒm) are m-selections, m ≦ w, of integers 1, …, n, then A [ω| ϒ] denotes the m-square generalized submatrix [aωiϒj], i, j = 1, …, m, of the n-square matrix A. If ω is an increasing m-combination, then A [ω|ω] is an m-square principal submatrix of A.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 982 - 991
Copyright
Copyright © Canadian Mathematical Society 1969

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