Geodesic
Some equalities for generalized inverses of matrix sums and block circulant matrices
Archivum mathematicum, Tome 37 (2001) no. 4, pp. 301-306 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 15A09, 15A23
Keywords: block circulant matrix; Moore-Penrose inverse; Drazin inverse; weighted Moore-Penrose inverse; quaternionic matrix 
@article{ARM_2001_37_4_a6,
     author = {Tian, Yongge},
     title = {Some equalities for generalized inverses of matrix sums and block circulant matrices},
     journal = {Archivum mathematicum},
     pages = {301--306},
     year = {2001},
     volume = {37},
     number = {4},
     mrnumber = {1879453},
     zbl = {1090.15005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2001_37_4_a6/}
}
TY  - JOUR
AU  - Tian, Yongge
TI  - Some equalities for generalized inverses of matrix sums and block circulant matrices
JO  - Archivum mathematicum
PY  - 2001
SP  - 301
EP  - 306
VL  - 37
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ARM_2001_37_4_a6/
LA  - en
ID  - ARM_2001_37_4_a6
ER  - 
%0 Journal Article
%A Tian, Yongge
%T Some equalities for generalized inverses of matrix sums and block circulant matrices
%J Archivum mathematicum
%D 2001
%P 301-306
%V 37
%N 4
%U http://geodesic.mathdoc.fr/item/ARM_2001_37_4_a6/
%G en
%F ARM_2001_37_4_a6
Tian, Yongge. Some equalities for generalized inverses of matrix sums and block circulant matrices. Archivum mathematicum, Tome 37 (2001) no. 4, pp. 301-306. http://geodesic.mathdoc.fr/item/ARM_2001_37_4_a6/

[1] Bell C. L.: Generalized inverses of circulant and generalized circulant matrices. Linear Algebra Appl. 39 (1981), 133–142. | MR | Zbl

[2] Ben-Israel A., Greville T. N. E.: Generalized Inverses: Theory and Applications. R. E. Krieger Publishing Company, New York, 1980. | MR | Zbl

[3] Davis P. J.: Circulant Matrices. Wiley, New York, 1979. | MR | Zbl

[4] Searle S. R.: On inverting circulant matrices. Linear Algebra Appl. 25 (1979), 77–89. | MR | Zbl

[5] Smith R. L.: Moore-Penrose inverses of block circulant and block $k$-circulant matrices. Linear Algebra Appl. 16 (1979), 237–245. | MR

[6] Tian Y.: The Moore-Penrose inverses of $ m \times n $ block matrices and their applications. Linear Algebra Appl. 283 (1998), 35–60. | MR | Zbl

[7] Tian Y.: Universal similarity factorization equalities over real Clifford algebras. Adv. Appl. Clifford Algebras 8 (1998), 365–402. | MR | Zbl