A new method for computing Moore–Penrose inverse through Gauss–Jordan elimination

Performing elementary row operations on [A|I], we can calculate matrices whose columns form bases for N(A)N(A) and N(A∗)N(A∗) easily. These matrices are then used to construct a bordered matrix through which the Moore–Penrose inverse A†A† of a general matrix AA can be obtained through further elementary row operations. Our method is reduced to the classical Gauss–Jordan elimination procedure for the regular inverse when applied to a nonsingular matrix. An example is included to illustrate the new method.