| Title:
|
Block diagonalization (English) |
| Author:
|
Koliha, J. J. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
237-246 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
eigenprojection |
| Keyword:
|
resolutions of the unit matrix |
| Keyword:
|
block diagonalization |
| Keyword:
|
Drazin inverse |
| MSC:
|
15A09 |
| MSC:
|
15A18 |
| MSC:
|
15A21 |
| MSC:
|
15A27 |
| idZBL:
|
Zbl 0982.15010 |
| idMR:
|
MR1826486 |
| DOI:
|
10.21136/MB.2001.133928 |
| . |
| Date available:
|
2009-09-24T21:49:39Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133928 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] J. J. Koliha, I. Straškraba: Power bounded and exponentially bounded matrices.Appl. Math. 44 (1999), 289–308. MR 1698770, 10.1023/A:1023032629988 |
| Reference:
|
[4] P. Lagerstrom: A proof of a theorem on commutative matrices.Bull. Amer. Math. Soc. 51 (1945), 535–536. Zbl 0060.03506, MR 0013120, 10.1090/S0002-9904-1945-08386-4 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] U. G. Rothblum: A representation of the Drazin inverse and characterizations of the index.SIAM J. Appl. Math. 31 (1976), 646–648. Zbl 0355.15008, MR 0422303, 10.1137/0131057 |
| Reference:
|
[9] U. G. Rothblum: Resolvent expansions of matrices and applications.Linear Algebra Appl. 38 (1981), 33–49. Zbl 0468.15002, MR 0636023 |
| Reference:
|
[10] D. A. Suprunenko, R. I. Tyshkevich: Commutative Matrices.Academic Press, New York, 1968. |
| Reference:
|
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| . |
