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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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A relationship between characteristic values and vectors
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by E. T. Beasley and P. M. Gibson PDF
Proc. Amer. Math. Soc. 43 (1974), 71-78 Request permission

Abstract:

It is shown that for all nonzero $n$-component column vectors $\alpha$ and $\beta$ over a field $F$ there exists a set $\Gamma$ of $n$-square matrices over $F$ of cardinality ${n^2} - 2n + 2$ such that, for each $n$-square matrix $A$ over $F,A\alpha = \alpha$ or ${A^T}\beta = \beta$ if and only if 1 is a characteristic value of PA for every $P \in \Gamma$.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 43 (1974), 71-78
  • MSC: Primary 15A18
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0340274-3
  • MathSciNet review: 0340274