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.