Jordan canonical form of a partitioned complex matrix and its application to real quaternion matrices

Citation data:

Communications in Algebra, ISSN: 0092-7872, Vol: 29, Issue: 6, Page: 2363-2375

Publication Year:
2001
Usage 54
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Repository URL:
https://nsuworks.nova.edu/math_facarticles/68; https://works.bepress.com/fuzhen-zhang/62
DOI:
10.1081/agb-100002394
Author(s):
Zhang, Fuzhen; Wei, Yimin
Publisher(s):
Informa UK Limited; NSUWorks
Tags:
Mathematics
article description
Let ∑ be the collection of all 2n × 2n partitioned complex matrices (A/-A A/A), where A and A are n × n complex matrices, the bars on top of them mean matrix conjugate. We show that ∑ is closed under similarity transformation to Jordan (canonical) forms. Precisely, any matrix in ∑ is similar to a matrix in the form J ⊗ J̄ ∈ ∑ via an invertible matrix in ∑, where J is a Jordan form whose diagonal elements all have nonnegative imaginary parts. An application of this result gives the Jordan form of real quaternion matrices.