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Proceedings of the American Mathematical Society

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

 
 

 

A relationship between characteristic values and vectors


Authors: E. T. Beasley and P. M. Gibson
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
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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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Article copyright: © Copyright 1974 American Mathematical Society