Can someone explain to me how should I solve this question?
Suppose
$S = << x_1,...,x_s>> $ $\subseteq$ $R^n$
$T = << y_1,...,y_t>> $ $\subseteq$ $R^n$
Assume that {$x_i$ | i = 1:s} and {$y_i$ | i = 1:t} are linearly independent sets. Use SVD to find a basis for S $\cap $ T.
I'm able to find the orthogonal basis for S and T respectively but I have no idea when it comes to the intersection of both S and T. Thanks in advance.
Please provide your partial answer on the orthonormal basis of $S$ and $T$, as it helps to provide an answer in terms you understand.
One of the properties you can use to determine the base for intersection $S \cap T$ is that any base vector of $T$ should preserve norm under multiplication by the normal base of $S$.
So I think you can multiply $V_S$ and $V_T$, limited to the non-zero singular values.