Block diagonalization. (English) Zbl 0982.15010

Koliha, J. J.

Math. Bohem. 126, No. 1, 237-246 (2001).

Summary: We study block diagonalization of matrices induced by resolutions of the unit matrix into the sum of idempotent matrices. We show that the block diagonal matrices have disjoint spectra if and only if each idempotent matrix in the inducing resolution double commutes with the given matrix. Applications include a new characterization of an eigenprojection and of the Drazin inverse of a given matrix.

MSC:

15A21	Canonical forms, reductions, classification
15A18	Eigenvalues, singular values, and eigenvectors
15A09	Theory of matrix inversion and generalized inverses
15A27	Commutativity of matrices

Keywords:

eigenprojection; resolutions of the unit matrix; block diagonalization; Drazin inverse