# A Comprehensive Note on Submatrix Constraint for Inverse Eigenvalue Problem of Symmetric Matrix

## Authors

Manpreet Kaur
Department of Mathematics, Chandigarh University, Mohali, Punjab, India-140413
Vineet Bhatt
Department of Mathematics, Chandigarh University, Mohali, Punjab, India-140413

### Synopsis

A matrix $$P\in \mathbb{R}^{n\times n}$$ is said to be $$(R,S)$$ symmetric matrix if $$RPS=P$$, where $$R, S$$ be nontrivial involutions. The conditions for solving the inverse eigenvalue problem with leading principal submatrix constraints using a $$(R, S)$$ symmetric matrix are derived. Additionally, the existence, uniqueness, and expression of the $$(R, S)$$ symmetric matrix solution to the inverse eigenvalue problem's best approximation problem. The problem's best approximation solution is computed using an algorithm that is also provided. A numerical example is provided to demonstrate the algorithm's viability.

Published
October 10, 2022