Finds the pseudoinverse matrix of a input matrix by using singular value decomposition. Use this node when Inverse Matrix cannot compute the inverse of a matrix, such as for rectangular or singular matrices.

## input matrix

A rectangular matrix.

This input also accepts square matrices, but Inverse Matrix can more efficiently calculate the actual inverse of a square matrix as long as the matrix is nonsingular.

Default: Empty array

## tolerance

A level such that the number of singular values greater than this level is the rank of input matrix.

If tolerance is negative, the node uses the following equation to determine the actual tolerance:

$\text{tolerance}=\text{\hspace{0.17em}}\text{max(}m,\text{\hspace{0.17em}}n\right)*‖A‖*\epsilon$ where

• A represents the input matrix
• m represents the number of rows in A
• n represents the number of columns in A
• $‖A‖$ is the 2-norm of A
• $\epsilon$ is the smallest floating point number that can be represented by type double

Default: -1

## pseudoinverse matrix

The pseudoinverse matrix of input matrix.

## error

A value that represents any error or warning that occurs when this node executes.