Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities

Details Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities

2007-09-04

arxiv.org/abs/0709.0513v1

Linear Algebra and Its Applications 428 (2008), 890-910

Mathematics

Commutative Algebra

26 pages, 2 tables and 2 figures. To appear in Linear Algebra and Its Applications

Scientific paper

We construct six unitary trace invariants for 2 by 2 quaternionic matrices which separate the unitary similarity classes of such matrices, and show that this set is minimal. We prove two quaternionic versions of a well known characterization of triangularizable subalgebras of matrix algebras over an algebraically closed field. Finally we consider the problem of describing the semi-algebraic set of pairs (X,Y) of quaternionic n by n matrices which are simultaneously triangularizable. Even the case n=2, which we analyze in more detail, remains unsolved.

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