Aaisha Be, Debasisha Mishra
This article introduces the Hartwig-Spindelböck decomposition of dual complex matrices. We provide representations of some generalized inverses using this decomposition. Further, several characterizations are established for a complex matrix to be Hermitian, normal and new dual EP matrix.
Aaisha Be, Debasisha Mishra
This paper contains 4 sections, 10 theorems, 23 equations.
Theorem 2.1
(Theorem $5.2$, qi2022arXiv) Let $\hat{A}\in \mathbb{DC}^{m\times n}$. Then, there exist dual complex unitary matrices $\hat{U}\in \mathbb{DC}^{m\times m}$ and $\hat{V}\in \mathbb{DC}^{n\times n}$ such that where $\hat{\Sigma}_{t}\in \mathbb{D}^{t\times t}$ is a dual diagonal matrix of the form $r\leq t \leq \min\{m,n\}$, $\hat{\mu}_1\geq\dots\geq \hat{\mu}_r$ are positive appreciable dual numbe
