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Probabilistic factorization of a quadratic matrix polynomial

Published online by Cambridge University Press:  24 October 2008

Joanne Kennedy  and
David Williams
Joanne Kennedy
Affiliation:
Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB
David Williams
Affiliation:
Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB
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Extract

A purely algebraic result. We begin by stating the following theorem. Theorem. Let E be a finite set, and letdenote the set of real E × E matrices with non-negative off-diagonal elements and with non-positive row sums. Let A be a symmetric element of, and let V be a diagonal real E × E matrix. Then there exists a unique pair (H+, H−) of elements ofsuch that

I denoting the identity E × E matrix, and the superscript T signifying transpose. It is an immediate consequence that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 3 , May 1990 , pp. 591 - 600
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

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