Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T00:35:49.522Z Has data issue: false hasContentIssue false
  • English
  • Français

Characteristic Polynomials

Published online by Cambridge University Press:  20 November 2018

Hans Schneider
Hans Schneider*
Affiliation:
Queen's University, Belfast and Washington State College Pullman, Wash.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let F be a field and let V be a finite dimensional vector space over F which is also a module over the ring F[a]. Here a may lie in any extension ring of F. We do not assume, as yet, that V is a faithful module, so that a need not be a linear transformation on V. It is known that by means of a decomposition of V into cyclic F[a]-modules we may obtain a definition of the characteristic polynomial of a on V which does not involve determinants.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 60 - 67
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Goddard, L. S. and Schneider, H., Matrices with a non-zero commutator, Proc. Cambridge Phil. Soc. 51 (1955), 551–553.Google Scholar
2. Goldhaber, J. K., The homomorphic mapping of certain matric algebras onto rings of diagonal matrices, Can. J. Math. 4 (1952), 31–42.Google Scholar
3. Goldhaber, J. K. and Whaples, G., On some matrix theorems of Frobenius and McCoy, Can. J. Math. 5 (1953), 332–335.Google Scholar
4. Jacobson, N., Lectures on abstract algebra, vol. 2 (New York, 1953).Google Scholar
5. Osborne, E. E., On matrices having the same characteristic equation, Pacific j . Math. 2 (1952), 227–230.Google Scholar