Abstract
Matrix generalized inverses and elementary transformation matrix is a very important operation.In solving equations, the inverse of matrix and matrix theory,it is playing a very important role.
In this paper, we briefly introduces the generalized inverse matrix and the matrix,the definition of generalized inverse matrix and its properties and calculation methods,and give examples of the various special cases and the non-exceptional circumstances how to solve Matrix Inverse.Then introduced two ways to solve the matrix equation AX = B, and gives some specific examples.
Generalized inverses in practical applications, for different purposes can define the generalized inverse different meaning, in other words we can also study the equation that satisfy part of the Penrose matrix equation.Set the matrix,with signs to show those set of all matrix that satisfy the Penrose matrix equation of the first i the first j,... first,l. Sign as any of a matrix in , called one reverse of A.
Keywords: generalized inverses matrix elementary transformation matrix equation Penrose equation
