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linalg::nullspace -- basis for the null space of a matrix

Introduction

linalg::nullspace(A) returns a basis for the null space of the matrix A, i.e., a list B of linearly independent vectors such that A*x=0 if and only if x is a linear combination of the vectors in B.

Call(s)

linalg::nullspace(A)

Parameters

A - a matrix of a domain of category Cat::Matrix

Returns

a list of (column) vectors of the domain Dom::Matrix(R), where R is the component ring of A.

Related Functions

linalg::basis, linalg::matlinsolve, linsolve, numeric::matlinsolve

Details

Example 1

The kernel of the matrix:

>> A := Dom::Matrix(Dom::Real)( 
     [[3^(1/2)*2 - 2, 2], [4, 3^(1/2)*2 + 2]] 
   )
                       +-                        -+
                       |     1/2                  |
                       |  2 3    - 2,      2      |
                       |                          |
                       |                 1/2      |
                       |       4,     2 3    + 2  |
                       +-                        -+

is one-dimensional, and a basis is {[-1/(sqrt(3)-1),1]}:

>> linalg::nullspace(A)
                          -- +-            -+ --
                          |  |       1      |  |
                          |  |  - --------  |  |
                          |  |     1/2      |  |
                          |  |    3    - 1  |  |
                          |  |              |  |
                          |  |       1      |  |
                          -- +-            -+ --

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