Characteristic free, improved decidability criteria for the similarity problem
Title:
Characteristic free, improved decidability criteria for the similarity problem
Author:
Gauger, Michael A. Byrnes, Christopher I.
Appeared in:
Linear & multilinear algebra
Paging:
Volume 5 (1977) nr. 3 pages 153-158
Year:
1977
Contents:
In [1], the authors derived algebraic criteria, expressible as a first order sentence in field theory, for the similarity of two matrices over a field of characteristic zero. It thus follows from a well-known result in model theory that this criteria is valid for sufficiently large characteristics, while all of our philosophy and techniques, save one, remain valid in arbitrary characteristics. The characteristic zero phenomenon is contained in the Clebsch-Gordan Theorem or rather in one of its consequences, Roth's Lemma. In order to avoid the use of Roth's Lemma, we have devised an alternate proof which also gives much more simplified criteria, valid in arbitrary characteristic and denned over nonalgebraically closed fields.
Journal description