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Member of the linalgebra class.

Syntax

c = pinv(a)

c = pinv(a, tol)

Description

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.

Examples

Inputs

Name	Description
a	Specifies a real rectangular or complex rectangular matrix.
tol	Specifies the 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, LabVIEW 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.

Outputs

Name	Description
c	Returns the pseudoinverse of a. c is a matrix.

Examples

A = [1, 0, 1; 0, 0, 4]
C = pinv(A)

Related Topics

inv
rank