A note on the unique solvability condition for generalized absolute value matrix equation

Shubham Kumar; Deepmala

doi:10.33993/jnaat511-1263

Authors

Shubham Kumar Indian Institute of Information Technology, Design and Manufacturing- PDPM, Jabalpur, India
Deepmala Indian Institute of Information Technology, Design and Manufacturing- PDPM, Jabalpur, India

DOI:

https://doi.org/10.33993/jnaat511-1263

Keywords:

Generalized absolute value matrix equation, unique solution, singular value, spectral radius

Abstract views: 431

Abstract

The spectral radius condition
\[\rho (\vert A^{-1} \vert\cdot \vert B \vert)<1\]
for the unique solvability of generalized absolute value matrix equation (GAVME)
\[AX + B \vert X \vert = D\]
is provided. For some instances, our condition is superior to the earlier published singular values conditions \(\sigma_{\max}(\vert B \vert)<\sigma_{\min}(A)\) [M. Dehghan, 2020] and \(\sigma_{\max}(B)<\sigma_{\min}(A)\) [Kai Xie, 2021]. For the validity of our condition, we also provided an example.

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References

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