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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An application of theorems of Schur and Albert
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by Thomas L. Markham PDF
Proc. Amer. Math. Soc. 59 (1976), 205-210 Request permission

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
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 59 (1976), 205-210
  • MSC: Primary 15A48; Secondary 15A57
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0432682-9
  • MathSciNet review: 0432682