A generalization of the notion of the inverse of a square matrix to other matrices. The pseudoinverse A+ of a matrix A is characterized by the properties
(i) AA+A = A and A+AA+= A+ (ii) AA+ and A+A are symmetric.
When A is invertible, A+ =A−1. Further, x0 = A+b minimizes |Ax–b| as x varies. See singular value decompostion.