Block diagonalization

Jaromír J. Koliha

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 1, page 237-246
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Koliha, Jaromír J.. "Block diagonalization." Mathematica Bohemica 126.1 (2001): 237-246. <http://eudml.org/doc/248848>.

@article{Koliha2001,
abstract = {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.},
author = {Koliha, Jaromír J.},
journal = {Mathematica Bohemica},
keywords = {eigenprojection; resolutions of the unit matrix; block diagonalization; Drazin inverse; eigenprojection; resolutions of the unit matrix; block diagonalization; Drazin inverse},
language = {eng},
number = {1},
pages = {237-246},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Block diagonalization},
url = {http://eudml.org/doc/248848},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Koliha, Jaromír J.
TI - Block diagonalization
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 1
SP - 237
EP - 246
AB - 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.
LA - eng
KW - eigenprojection; resolutions of the unit matrix; block diagonalization; Drazin inverse; eigenprojection; resolutions of the unit matrix; block diagonalization; Drazin inverse
UR - http://eudml.org/doc/248848
ER -

References

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  7. Matrix Algebra Using MINImal MATlab, A. K. Peters, Wellesley, 1995. (1995) Zbl0817.15001MR1311706
  8. 10.1137/0131057, SIAM J. Appl. Math. 31 (1976), 646–648. (1976) Zbl0355.15008MR0422303DOI10.1137/0131057
  9. Resolvent expansions of matrices and applications, Linear Algebra Appl. 38 (1981), 33–49. (1981) Zbl0468.15002MR0636023
  10. Commutative Matrices, Academic Press, New York, 1968. (1968) 
  11. Lectures on Matrices, AMS Colloq. Publ. 17, Amer. Math. Soc., Providence, 1934. (1934) Zbl0010.09904MR0168568

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