Jordan Canonical Form of a Partitioned Complex Matrix and Its Applications to Real Quaternion Matrices
Communications in Algebra
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.
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.