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:
- Repository URL:
- https://nsuworks.nova.edu/math_facarticles/68; https://works.bepress.com/fuzhen-zhang/62
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.