null

Form basis for null space of matrix

Syntax

Z = null(A)

Description

Z = null(A) returns a list of vectors that form the basis for the null space of a matrix A. The product A*Z is zero. size(Z, 2) is the nullity of A. If A has full rank, Z is empty.

example

Examples

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Form Basis for Null Space of Matrix

Find the basis for the null space and the nullity of the magic square of symbolic numbers. Verify that A*Z is zero.

A = sym(magic(4));
Z = null(A)
nullityOfA = size(Z, 2)
A*Z

Z =
 -1
 -3
  3
  1

nullityOfA =
     1

ans =
 0
 0
 0
 0

Form Basis for Null Space of Matrix of Full Rank

Find the basis for the null space of the matrix B that has full rank.

B = sym(hilb(3))
Z = null(B)

B =
[   1, 1/2, 1/3]
[ 1/2, 1/3, 1/4]
[ 1/3, 1/4, 1/5]
 
Z =
Empty sym: 1-by-0

Input Arguments

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`A` — Input
numeric matrix | symbolic matrix

Input, specified as a numeric or symbolic matrix.

Version History

Introduced before R2006a