Relative linear sets and similarity of matrices whose elements belong to a division algebra
| Autor: | M. C. Wolf, M. H. Ingraham |
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| Rok vydání: | 1937 |
| Předmět: | |
| Zdroj: | Transactions of the American Mathematical Society. 42:16-31 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/s0002-9947-1937-1501911-2 |
| Popis: | It is the purpose of this paper to develop the theory of the similarity transformation for matrices whose elements belong to a division algebra. In order to get a basis for generalization, the theory of the similarity transformation for matrices whose elements belong to a field is sketched in what seems to the authors a more suggestive method than those used heretofore.: L. A. Wolf's paper entitled Similarity of matrices in which the elements are real quaternions? treats the case of the quaternion algebra over any subfield of the real field, by passing to the equivalent square matrices of order 2n with elements in the subfield. Some of the results of the present paper are given in an abstract and a subsequent paper by N. Jacobson.II Jacobson's results are to a certain extent more general. In the present paper a usable rational process is given for determining the equivalence or non-equivalence of matrices whose elements belong to a division algebra, and a theorem is developed concerning the rank of a polynomial in a matrix, which is not indicated by Jacobson. Some of the results contained herein were given by Ingraham at the summer meeting of the Society in 1935.? |
| Databáze: | OpenAIRE |
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