Computes the rank of a matrix.

## input matrix

A matrix.

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

## rank

The number of singular values in the input matrix that are larger than the tolerance. rank is the maximum number of independent rows or columns in the input matrix.

## error

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