Mathematics Faculty Articles

Title

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

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.

DOI

10.1081/AGB-100002394

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