| Title:
|
Some equalities for generalized inverses of matrix sums and block circulant matrices (English) |
| Author:
|
Tian, Yongge |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
301-306 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $ A_1, A_2,\cdots , A_n $ be complex matrices of the same size. We show in this note that the Moore-Penrose inverse, the Drazin inverse and the weighted Moore-Penrose inverse of the sum $ \sum _{t=1}^{n} A_t$ can all be determined by the block circulant matrix generated by $ A_1, A_2, \cdots , A_n$. In addition, some equalities are also presented for the Moore-Penrose inverse and the Drazin inverse of a quaternionic matrix. (English) |
| Keyword:
|
block circulant matrix |
| Keyword:
|
Moore-Penrose inverse |
| Keyword:
|
Drazin inverse |
| Keyword:
|
weighted Moore-Penrose inverse |
| Keyword:
|
quaternionic matrix |
| MSC:
|
15A09 |
| MSC:
|
15A23 |
| idZBL:
|
Zbl 1090.15005 |
| idMR:
|
MR1879453 |
| . |
| Date available:
|
2008-06-06T22:29:21Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107808 |
| . |
| Reference:
|
[1] Bell C. L.: Generalized inverses of circulant and generalized circulant matrices.Linear Algebra Appl. 39 (1981), 133–142. Zbl 0465.15003, MR 0625244 |
| Reference:
|
[2] Ben-Israel A., Greville T. N. E.: Generalized Inverses: Theory and Applications.R. E. Krieger Publishing Company, New York, 1980. Zbl 0451.15004, MR 0587113 |
| Reference:
|
[3] Davis P. J.: Circulant Matrices.Wiley, New York, 1979. Zbl 0418.15017, MR 0543191 |
| Reference:
|
[4] Searle S. R.: On inverting circulant matrices.Linear Algebra Appl. 25 (1979), 77–89. Zbl 0397.15004, MR 0528714 |
| Reference:
|
[5] Smith R. L.: Moore-Penrose inverses of block circulant and block $k$-circulant matrices.Linear Algebra Appl. 16 (1979), 237–245. MR 0469933 |
| Reference:
|
[6] Tian Y.: The Moore-Penrose inverses of $ m \times n $ block matrices and their applications.Linear Algebra Appl. 283 (1998), 35–60. Zbl 0932.15004, MR 1657194 |
| Reference:
|
[7] Tian Y.: Universal similarity factorization equalities over real Clifford algebras.Adv. Appl. Clifford Algebras 8 (1998), 365–402. Zbl 0926.15026, MR 1698292 |
| . |
