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On the Schur product of H-matrices and non-negative matrices, and related inequalities

Published online by Cambridge University Press:  24 October 2008

M. S. Lynn
M. S. Lynn
Affiliation:
Mathematics Division, National Physical Laboratory
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Extract

1. Introduction. Let ℛn denote the set of all n × n matrices with real elements, and let denote the subset of ℛn consisting of all real, n × n, symmetric positive-definite matrices. We shall use the notation to denote that minor of the matrix A = (aij) ∈ ℛn which is the determinant of the matrix

The Schur Product (Schur (14)) of two matrices A, B ∈ ℛn is denned by

where A = (aij), B = (bij), C = (cij) and

Let ϕ be the mapping of ℛn into the real line defined by

for all A ∈ ℛn, where, as in the sequel, .

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 3 , July 1964 , pp. 425 - 431
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

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