Let $A\in M_n$ and $s_j$ be singular value of $A$ with associated left singular vectors $u_1,u_2,....u_n$ and associated right singular vectors $v_1,v_2,....v_n$
Suppose $T=[u_1,...,u_n][v_1,...,v_n]^*$
Why does $Tv_j=u_j$?
(for all $j$)
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Sign up to join this communityHint: $T = UV^*$, and $v_j = Ve_j$ where $e_j$ denotes the $j$th standard basis vector