Determinant, inertia, and inverse of a class of irreducible tridiagonal matrices
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Cristian Conde
,
Ezequiel Dratman
Abstract
In this paper, we study a class of irreducible tridiagonal matrices and analyze their fundamental properties. We derive explicit formulas for their determinant, providing insights into their spectral behavior. Additionally, we establish results concerning their inertia and obtain closed-form expressions for their inverse. These findings contribute to the broader understanding of structured matrices and have potential applications in various fields of mathematics and other sciences.
Funding statement: The present work was supported by PIP2022-2024 GI-11220210100392CO, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina.
Acknowledgements
The authors sincerely thank the referee for the careful reading of the manuscript and for the valuable comments and suggestions, which have helped us to improve the quality and clarity of the paper.
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