MERAHI, WARDA
(2019)
*Étude de systèmes linéaires par inversion généralisée.*
Doctoral thesis, Université de Batna 2.

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## Abstract

a powerful tool for solving matrix equations and establishing various rank equalities or inequalities for matrices. This work is divided into three parts, organized as follows. In the first one, we study the common hermitian solution of matrix equation A1XA∗1 = B1 and A2XA∗2 = B2, and we provide necessary and sufficient conditions to have a common hermitian solution in the form X = X1 + X2 2 , where X1 and X2 are the solution of A1XA∗1 = B1 and A2XA∗2 = B2 respectively. In addition, we determine maximal and minimal ranks of submatrices in a common hermitian solution and other results are established. In the second part, we give some formulas for the maximal and minimal ranks of A ± D1X1D∗ 1 ± D2X2D∗ 2 subject to the hermitian solutions of a consistent matrix equations A1X1A∗1 = B1 and A2X2A2∗ = B2 , from these formulas we establish characterizations of some classes of solutions of the given equations. In the third part, our work is concerned with additive decomposition of least rank solution of the matrix equations AXB = C and AXA∗ = B .

Item Type: | Thesis (Doctoral) |
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Uncontrolled Keywords: | Moore-Penrose inverse, matrix equation, hermitian solution, submatrix, rank of a matrix. |

Subjects: | Mathématiques |

Divisions: | Faculté des mathématiques et de l'informatique > Département des mathématiques |

Date Deposited: | 25 Jul 2019 09:28 |

Last Modified: | 25 Jul 2019 09:28 |

URI: | http://eprints.univ-batna2.dz/id/eprint/1764 |

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