Revies study on solving the singular linear algebraic systems using the Drazin inverse of the matrix

Abstract EN

By the Drazin inverse of given matrix, we mean a matrix that exists for a square singular matrix that has some of the properties of the multiplicative inverse of matrices and that agrees with it when given matrix is non-singular, that means the index of a given matrix equals zero.

Study the linear algebraic systems is one of the important study fields of linear algebra.

We consider the singular linear algebraic systems on the form ?? = ?, where ? ∈ ℂ ?×? is singular, and ?, ? are vectors in ℂ ?.

We study solving these systems using the Drazin inverse of the matrix.

For that, we give the general solution, the generalized least squares solution and the unique minimal least squares solution for a given system.

The results are taken from the mentioned references.

We give some examples to illustrate our study.