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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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DOI: https://doi.org/10.1090/S0002-9939-1974-0340274-3
Article copyright: © Copyright 1974 American Mathematical Society

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