Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities |
| |
Authors: | Dragomir ?. Dokovi? Benjamin H. Smith |
| |
Affiliation: | Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 |
| |
Abstract: | We construct six unitary trace invariants for 2×2 quaternionic matrices which separate the unitary similarity classes of such matrices, and show that this set is minimal. We have discovered a curious trace identity for two unit-speed one-parameter subgroups of Sp(1). A modification gives an infinite family of trace identities for quaternions as well as for 2×2 complex matrices. We were not able to locate these identities in the literature. 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×n matrices which are simultaneously triangularizable. Even the case n=2, which we analyze in more detail, remains unsolved. |
| |
Keywords: | 15A33 15A18 16R30 |
本文献已被 ScienceDirect 等数据库收录! |
|