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arXiv · 2204.09861

Dual $r$-Rank Decomposition and Its Applications

Hongxing Wang·Chong Cui·Xiaoji Liu
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Abstract

In this paper, we introduce the dual $r$-rank decomposition of dual matrix, get its existence condition and equivalent form of the decomposition, as well as derive some characterizations of dual Moore-Penrose generalized inverse(DMPGI). Based on DMPGI, we introduce one special dual matrix(dual EP matrix). By applying the dual $r$-rank decomposition we derive several characterizations of dual EP matrix, dual idempotent matrix, dual generalized inverses, and the relationships among dual Penrose equations.

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Hongxing Wang, Chong Cui, Xiaoji Liu. 2022-04-21. Dual $r$-Rank Decomposition and Its Applications. https://arxiv.org/abs/2204.09861

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