Form basis for null space of matrix
Z = null(A)
example
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.
A
A*Z
size(Z, 2)
Z
collapse all
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
Find the basis for the null space of the matrix B that has full rank.
B
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, specified as a numeric or symbolic matrix.
rank | rref | svd
rank
rref
svd