# Does the Generalized Inverse of $A$ Commute with $A$?

by Edward T. Wong (Oberlin College)

Mathematics Magazine
October, 1986

Subject classification(s): Algebra and Number Theory | Linear Algebra | Inner Product Spaces

Not all square matrices commute with their generalized inverse (Moore-Penrose inverse). The author gathers equivalent conditions for the generalized inverse of a matrix to commute with the matrix itself. Then he shows that, in this case, the generalized inverse may be represented as a polynomial in the given matrix.

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Capsule Course Topic(s):
Linear Algebra | Matrix Invertibility