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# Pseudoinverse

Compute Moore-Penrose pseudoinverse of matrix

## Library

Math Functions / Matrices and Linear Algebra / Matrix Inverses

dspinverses

## Description

The Pseudoinverse block computes the Moore-Penrose pseudoinverse of input matrix A.

[U,S,V] = svd(A,0)							% Equivalent MATLAB code

The pseudoinverse of A is the matrix ${A}^{†}$ such that

${A}^{†}=V{S}^{†}{U}^{\ast }$

where U and V are orthogonal matrices, and S is a diagonal matrix. The pseudoinverse has the following properties:

• $A{A}^{†}={\left(A{A}^{†}\right)}^{\ast }$

• ${A}^{†}A={\left({A}^{†}A\right)}^{\ast }$

• $A{A}^{†}A=A$

• ${A}^{†}A{A}^{†}={A}^{†}$

## Dialog Box

Show error status port

Select to enable the E output port, which reports a failure to converge. The possible values you can receive on the port are:

• 0 — The pseudoinverse calculation converges.

• 1 — The pseudoinverse calculation does not converge.

If the pseudoinverse calculation fails to converge, the output at port X is an undefined matrix of the correct size.

## References

Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.

## Supported Data Types

PortSupported Data Types

A

• Double-precision floating point

• Single-precision floating point

X

• Double-precision floating point

• Single-precision floating point

E

• Boolean

## See Also

 Cholesky Inverse DSP System Toolbox LDL Inverse DSP System Toolbox LU Inverse DSP System Toolbox Singular Value Decomposition DSP System Toolbox inv MATLAB

See Matrix Inverses for related information.

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