Nullspace of a matrix via its SVD

Returning to this example, involving a matrix with row size m = 4 and column size n = 5 , and of rank r = 3 . The nullspace is the span of the last n-r=2 columns of the 5 times 5 matrix : $mathbf{N}(A) = mbox{bf span} (v_4, v_5)$ , with

$v_4 := left(begin{array}{c} 0 0 0 1 0 end{array}right), ;; v_5 := left(begin{array}{c} -sqrt{0.8} 0 0 0 sqrt{0.2} end{array}right)$

We can check that Av_4 = Av_5 = 0 .

See also: this example.