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The core inverse and constrained matrix approximation problem
Open Mathematics ( IF 1.0 ) Pub Date : 2020-01-01 , DOI: 10.1515/math-2020-0178
Hongxing Wang 1 , Xiaoyan Zhang 1
Affiliation  

Abstract In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse: | | M x − b | | F = min subject to x ∈ ℛ ( M ) , ||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in {\mathcal R} (M), where M ∈ ℂ n CM M\in {{\mathbb{C}}}_{n}^{\text{CM}} . We get the unique solution to the problem, provide two Cramer’s rules for the unique solution and establish two new expressions for the core inverse.

中文翻译:

核心逆和约束矩阵逼近问题

摘要 在本文中,我们通过使用核逆来研究 Frobenius 范数中的约束矩阵逼近问题: | | M x − b | | F = minsubject to x ∈ ℛ ( M ) , ||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em} \text{to}\hspace{1em}x\in {\mathcal R} (M),其中 M ∈ ℂ n CM M\in {{\mathbb{C}}}_{n}^{\text{CM }} 。我们得到了问题的唯一解,为唯一解提供了两个克莱默规则,并为核心逆建立了两个新的表达式。
更新日期:2020-01-01
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