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Computes the pseudoinverse of a matrix. The m-by-n matrix A+ is the pseudoinverse of matrix A if A+ satisfies the following four Moore-Penrose conditions:

A A+A = A

A+A A+= A+

A A+ is a symmetric matrix.

A +A is a symmetric matrix.

## Syntax

c = pinv(a)
c = pinv(a, tol)

## a

Real rectangular or complex rectangular matrix.

## tol

Tolerance. The number of singular values greater than tol is the rank of a. tol is a real number. The default is -1. If tol is negative, MathScript sets the tolerance using the following equation: tol = max(m, n)*||A||* eps, where A is the input matrix, m is the number of rows in A, n is the number of columns in A, ||A|| is the 2-norm of A, and eps is the smallest, floating-point number such that 1+ eps>1. eps is defined by the following equation: eps= 2^(-52) = 2.22e-16.

## c

Pseudoinverse of a. c is a matrix.