关于复方阵的两个正交投影组合的可逆性和群逆

2017 Ninth International Conference on Advanced Computational Intelligence (ICACI) Pub Date : 2017-02-01 DOI:10.1109/ICACI.2017.7974479

Yinlan Chen

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引用次数: 0

摘要

对任意复方阵A，利用A的M-C-S分解，刻画了组合P = a1 PR(A) + a2 PR(A∗)+a3 PR(A) PR(A∗)+a4 PR(A∗)PR(A)的可逆性和群逆，给出了其可逆性及其逆的充分必要条件。此外，我们还刻画了群逆的性质，并给出了P是群可逆时p#的表达式。

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On invertibility and group inverse of combinations of two orthogonal projectors about a complex square matrix

For any complex square matrix A, this paper characterizes the invertibility and group inverse of the combinations P = a1 PR(A) + a2 PR(A∗) +a3 PR(A) PR(A∗) +a4 PR(A∗) PR(A) by M-C-S decomposition of A. Necessary and sufficient conditions of the invertibility and its inverse are presented completely. Also, we characterize the group inverse and give an expression for P^# when P is group invertible.

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2017 Ninth International Conference on Advanced Computational Intelligence (ICACI)

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