A Trace Condition Equivalent to Simultaneous Triangularizability
- 1 April 1986
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 38 (2), 376-386
- https://doi.org/10.4153/cjm-1986-018-1
Abstract
A collection of matrices over a field F is said to be triangularizable if there is an invertible matrix T over F such that the matrices T−1ST, are all upper triangular. It is a well-known and easy fact that any commutative set is triangularizable if F is algebraically closed, or if F contains the spectrum of every member of . Many sufficient conditions are known for triangularizability of matrix collections. Levitzki [7] proved that a (multiplicative) semigroup of nilpotent matrices is triangularizable. (His result is valid even over a division ring.) Kolchin [5] showed the triangularizability of a semigroup of unipotent matrices, i.e., matrices of the form I + N with N nilpotent. Kaplansky [3, 4] unified and generalized these results.Keywords
This publication has 2 references indexed in Scilit:
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- Lectures in Abstract AlgebraPublished by Springer Nature ,1953