# Determinant (G Dataflow)

Computes the determinant of a matrix.

## matrix type

Type of the input matrix.

Specifying the matrix type allows this node to execute more quickly by avoiding unnecessary computations, which could introduce numerical inaccuracy.

Name Description
General

The input matrix is a matrix that you cannot describe with one of the other categories.

Positive definite

The input matrix is positive-definite.

Lower triangular

The input matrix is lower triangular.

Upper triangular

The input matrix is upper triangular.

Default: General

## matrix

A square matrix.

This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## determinant

The determinant of the input matrix.

The determinant of a singular matrix is zero. This is a valid result and is not an error.

## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm for Calculating the Determinant

Let A be a square matrix that represents the input matrix, and let L and U represent the lower and upper triangular matrices, respectively, of A such that

A = LU

where the main diagonal elements of the lower triangular matrix L are arbitrarily set to one. This node finds the output determinant of A by the product of the main diagonal elements of the upper triangular matrix U.

$|A|=\underset{i=0}{\overset{n-1}{\prod }}{u}_{ii}$

where |A| is the output determinant of A and n is the dimension of A.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported