Left singular vector
= Left singular vector
{title2=$u_j$}
A unit left singular vector of a <matrix> or <compact operator> $A$ is an <eigenvector> of $AA^*$ with <eigenvalue> $\sigma_j^2$. For $\sigma_j>0$, it pairs with a <right singular vector> $v_j$ through $Av_j=\sigma_j u_j$ and $A^*u_j=\sigma_j v_j$.