Document Type : Research Paper

Authors

• M. Nikuie ¹
• A. Zohri ²
• M.K. Mirnia ³

¹ aYoung Researchers and Elite Club, Islamic Azad University, Tabriz Branch, Tabriz, IRAN.

² Payame Noor University, IRAN.

³ Department of Computer Sinence, Islamic Azad University, Tabriz Branch, Tabriz, IRAN.

Abstract

A matrix has an ordinary inverse only if it is square, and even then only if it is nonsingular or, in other words, if its columns (or rows) are linearly independent. In recent years needs have been felt in numerous areas of applied mathematics for some kind of partial inverse of a matrix that is singular or even rectangular. In this paper, some results on the Quasi-commuting inverses, are given and the effect of them in solving the case of linear system of equations where the coefficient matrix is a singular matrix, is illustrated.

Keywords

• Index of matrix
• Generalized inverse
• Singular linear system
• Quasi-commuting inverses