(untitled) (Journal of Computational Mathematics, 2021)
This paper proves a Kantorovich-type inequality on the matrix of the type 12(Q^H_1 AQ_1 Q^H_1A^-1 Q_1+Q^H_1A^-1Q_1Q^H_1AQ_1), where A is an n× n positive definite Hermitian matrix and Q_1 is an n× m matrix with rank (Q_1)=m. The result is applied to get an extension of the Bauer-Fike inequality on condition numbers of similarities that block diagonalized matrices.