Eigenvectors and maximal vectors in Boolean vector spaces

Sinzdak, Ronald L.

doi:10.1090/S0002-9939-1975-0357452-0

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Eigenvectors and maximal vectors in Boolean vector spaces
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by Ronald L. Sinzdak PDF

Proc. Amer. Math. Soc. 47 (1975), 323-328 Request permission

Abstract:

In this paper it is shown that every idempotent, self-adjoint linear endomorphism in a finite-dimensional normed Boolean vector space has its norm as an eigenvalue. A completely algebraic proof is also given for the fact that every linear endomorphism in such a space possesses a maximal vector.

References

P. V. Jagannadham, Linear transformations in a Boolean vector space, Math. Ann. 167 (1966), 240–247. MR 201355, DOI 10.1007/BF01361188
D. E. Rutherford, The eigenvalue problem for Boolean matrices, Proc. Roy. Soc. Edinburgh Sect. A 67 (1963/65), 25–38. MR 186597
N. V. Subrahmanyam, Boolean vetor spaces. I, Math. Z. 83 (1964), 422–433. MR 169800, DOI 10.1007/BF01111003
N. V. Subrahmanyam, Boolean vector spaces. II, Math. Z. 87 (1965), 401–419. MR 172825, DOI 10.1007/BF01111721

Additional Information

Journal: Proc. Amer. Math. Soc. 47 (1975), 323-328
DOI: https://doi.org/10.1090/S0002-9939-1975-0357452-0
MathSciNet review: 0357452