znu - Null-Space

Command Line

znu Options [-G] Matrix [NullSpace]

Options

Standard options, see Standard Command Line Options

-G

Output in GAP format.

Matrix

The matrix.

NullSpace

The null-space.

Input Files

Matrix

The matrix (M×N).

Output Files

NullSpace

The null-space, a L×M matrix in echelon form.

Description

This program reads in a matrix and outputs a basis for its null-space in echelon form. If the Nullspace argument is omitted the null-space is not written out, but its dimension is still printed.

Notice that the input matrix does not need to be square.

Implementation Details

After reading the matrix, the program generates the n×n identity matrix in memory where n is the number of rows. It then proceeds to perform row operations on the matrix until it is in echelon form. The same row operations are performed on the identity matrix, and whenever a row in the original matrix becomes zero, the corresponding row of the other matrix is marked for output. The null-space is always reduced to echelon form.