null

Orthonormal basis of the null space of a matrix.

Category: Mathematics > Linear Algebra

Syntax

Z = null(A)

Description

The null space is the set of vectors x with A*x = 0. null computes it from the singular value decomposition, treating singular values below a tolerance as zero, so the result is a numerical rank decision.

The basis is not unique: signs and rotations within the space vary. Check A*Z near zero instead of comparing entries with a reference.

Input arguments

A

Matrix.

Output arguments

Z

Matrix whose columns span the null space; it has n - rank(A) columns, and is empty when A has full column rank.

Example

A rank-one matrix

A = [1 1; 1 1];
Z = null(A)
disp(norm(A*Z) < 1e-12)
null(eye(2))

Z = 2×1

   -0.7071
    0.7071
   1
ans = 2×0 empty double matrix

See also

orth rank svd pinv lsqminnorm