## View abstract

### Session S08 - Inverse Problems and Applications

Wednesday, July 14, 18:50 ~ 19:20 UTC-3

## A review on Procrustes problems for matrix inverse eigenvalue problems

### Silvia Gigola

Given a matrix $X$ and a diagonal matrix $D$, we are looking for solutions of the equation $AX =XD$, where $A$ is a matrix with a prescribed structure and a predefined spectrum. Based on these restrictions on matrix $A$, a variety of inverse eigenvalue problems arises.
We will show the existence of the solutions of the inverse eigenvalue problem and the associated Procrustes problem for three kind of matrices: Hermitian reflexive matrices with respect to a normal and ${k+1}$-potent matrix, normal $J$-Hamiltonian matrices, and normal $J$-skew Hamiltonian matrices.