Sufficient conditions for the unique solvability of absolute value matrix equations

2023/05/08 by Shubham Kumar, Kumar, Shubham, Deepmala Deepmala +1
Computer Science · #15A06 #15A18 #90C30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2305.04495

openalex publication_date 2023/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we discussed the unique solvability of the two absolute value matrix equations. The unique solvability condition ρ(\vert A^-1 B \vert)<1 is provided for the generalized absolute value matrix equation (GAVME) AX + B \vert X \vert = F. This condition is superior to that of Kumar et al. [J. Numer. Anal. Approx. Theory, 51(1) (2022) 83-87]. We also discussed different conditions for the unique solvability of the new generalized absolute value matrix equation (NGAVME) AX+B\vert CX \vert=F with A, B, C, F, X ∈ R^{n × n}. We also provided the corrected version of Corollary 2.1 from the published work by Wang et al. [Appl. Math. Lett., 116 (2021) 106966].

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