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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An application of theorems of Schur and Albert


Author: Thomas L. Markham
Journal: Proc. Amer. Math. Soc. 59 (1976), 205-210
MSC: Primary 15A48; Secondary 15A57
MathSciNet review: 0432682
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Abstract: Suppose $ {\Pi _n}$ is the cone of $ n \times n$ positive semidefinite matrices, and $ \operatorname{int} ({\Pi _n})$ is the set of positive definite matrices. Theorems of Schur and Albert are applied to obtain some elements of $ {\Pi _n}$ and $ \operatorname{int} ({\Pi _n})$. Then an analogue of Albert's theorem is given for $ M$-matrices, and finally a generalization is given for matrices of class $ P$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0432682-9
PII: S 0002-9939(1976)0432682-9
Keywords: Positive semidefinite, positive definite, Schur complement, $ M$-matrices, class $ P$
Article copyright: © Copyright 1976 American Mathematical Society