Some equalities for generalized inverses of matrix sums and block circulant matrices

Yong Ge Tian

Archivum Mathematicum (2001)

  • Volume: 037, Issue: 4, page 301-306
  • ISSN: 0044-8753

Abstract

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Let A 1 , A 2 , ⋯ , 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 ∑ t = 1 n A t can all be determined by the block circulant matrix generated by A 1 , A 2 , ⋯ , A n . In addition, some equalities are also presented for the Moore-Penrose inverse and the Drazin inverse of a quaternionic matrix.

How to cite

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Tian, Yong Ge. "Some equalities for generalized inverses of matrix sums and block circulant matrices." Archivum Mathematicum 037.4 (2001): 301-306. <http://eudml.org/doc/248752>.

@article{Tian2001,
abstract = {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.},
author = {Tian, Yong Ge},
journal = {Archivum Mathematicum},
keywords = {block circulant matrix; Moore-Penrose inverse; Drazin inverse; weighted Moore-Penrose inverse; quaternionic matrix; block circulant matrix; Moore-Penrose inverse; Drazin inverse; weighted Moore-Penrose inverse; quaternionic matrix},
language = {eng},
number = {4},
pages = {301-306},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some equalities for generalized inverses of matrix sums and block circulant matrices},
url = {http://eudml.org/doc/248752},
volume = {037},
year = {2001},
}

TY - JOUR
AU - Tian, Yong Ge
TI - Some equalities for generalized inverses of matrix sums and block circulant matrices
JO - Archivum Mathematicum
PY - 2001
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 037
IS - 4
SP - 301
EP - 306
AB - 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.
LA - eng
KW - block circulant matrix; Moore-Penrose inverse; Drazin inverse; weighted Moore-Penrose inverse; quaternionic matrix; block circulant matrix; Moore-Penrose inverse; Drazin inverse; weighted Moore-Penrose inverse; quaternionic matrix
UR - http://eudml.org/doc/248752
ER -

References

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  1. Bell C. L., Generalized inverses of circulant and generalized circulant matrices, Linear Algebra Appl. 39 (1981), 133–142. (1981) Zbl0465.15003MR0625244
  2. Ben-Israel A., Greville T. N. E., Generalized Inverses: Theory and Applications, R. E. Krieger Publishing Company, New York, 1980. (1980) Zbl0451.15004MR0587113
  3. Davis P. J., Circulant Matrices, Wiley, New York, 1979. (1979) Zbl0418.15017MR0543191
  4. Searle S. R., On inverting circulant matrices, Linear Algebra Appl. 25 (1979), 77–89. (1979) Zbl0397.15004MR0528714
  5. Smith R. L., Moore-Penrose inverses of block circulant and block k -circulant matrices, Linear Algebra Appl. 16 (1979), 237–245. (1979) MR0469933
  6. Tian Y., The Moore-Penrose inverses of m × n block matrices and their applications, Linear Algebra Appl. 283 (1998), 35–60. (1998) Zbl0932.15004MR1657194
  7. Tian Y., Universal similarity factorization equalities over real Clifford algebras, Adv. Appl. Clifford Algebras 8 (1998), 365–402. (1998) Zbl0926.15026MR1698292

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