Jordan Canonical Form of a Partitioned Complex Matrix and Its Applications to Real Quaternion Matrices

Authors

Fuzhen Zhang, Nova Southeastern UniversityFollow
Yimin Wei, Fudan University

Document Type

Article

Publication Date

1-1-2001

Publication Title

Communications in Algebra

ISSN

0092-7872

Volume

29

Issue/No.

6

First Page

2363

Last Page

2375

Abstract

Let Σ be the collection of all 2n × 2n partitioned complex matrices

where A 1 and A 2 are n × n complex matrices, the bars on top of them mean matrix conjugate. We show that Σ is closed under similarity transformation to Jordan (canonical) forms. Precisely, any matrix in Σ is similar to a matrix in the form J ⊕

∈ Σ via an invertible matrix in Σ, where J is a Jordan form whose diagonalelements all have nonnegative imaginary parts. An application of this result gives the Jordan form of real quaternion matrices.

NSUWorks Citation

Zhang, Fuzhen and Wei, Yimin, "Jordan Canonical Form of a Partitioned Complex Matrix and Its Applications to Real Quaternion Matrices" (2001). Mathematics Faculty Articles. 68.
https://nsuworks.nova.edu/math_facarticles/68

DOI

10.1081/AGB-100002394