If A A U sigma V find an orthogonal basis for the range of

If A A = U sigma V*, find an orthogonal basis for the range of A and the null space of A*.

Solution

ANSWER :-

a)

If there are p non-zero singular values, then the first p Columns of U span the range of A.

b)

If there are p non zero singular values,then the last n-p columns of V span the kernel of A.

If p = n , A has no kernel.