On a class of non-Hermitian matrices with positive definite Schur complements

Berger, Thomas GND; Giribet, Juan; Martínez Pería, Francisco; Trunk, Carsten GND

Given a positive definite nXn matrix A and a Hermitian mXm matrix D, we characterize under which conditions there exists a strictly contractive matrix K such that the non-Hermitian block-matrix with the enties A and -AK in the first row and K^*A and D in the second has a positive definite Schur complement with respect to its submatrix A. Additionally, we show that K can be chosen such that diagonalizability of the block-matrix is guaranteed and we compute its spectrum. Moreover, we show a connection to the recently developed frame theory for Krein spaces.

Cite

Citation style:
Berger, T., Giribet, J., Martínez Pería, F., Trunk, C., 2018. On a class of non-Hermitian matrices with positive definite Schur complements.
Could not load citation form. Default citation form is displayed.

Rights

Use and reproduction:
All rights reserved

Export