The core inverse and constrained matrix approximation problem

2019/08/29 by Hongxing Wang, Xiaoyan Zhang, Wang, Hongxing +1
Computer Science · Mathematics · #15A24 #15A29 #15A57 #Advanced Optimization Algorithms Research #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1908.11077

openalex publication_date 2019/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper,we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse:‖Mx - b ‖_F=min \rm subject to x\inR(M) , where M∈ℂ^CM_n. 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.

Citations

• Characterizations of the core inverse and the core partial ordering
• Pseudo core inverses in rings with involution

Related

• Generalized rank-constrained matrix approximations
• On the Frobenius norm of the inverse of a non-negative matrix
• Core inverse of matrices
• Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms
• Concentration of the Frobenius norm of generalized matrix inverses