Given any $k$-tupel of linearly independent vectors $X$ as above, there exists a $k$-tuple $Y$ biorthognal to it. If $k=n$, this $Y$ is unique.
解答: Since $$ex ank(X^*X)= ank(X)=k, eex$$ there exists an unique $Ain M_k$ such that $$ex X^*XA=I_k. eex$$ Take $Y=XA$, we are completed.