Singular system of a compact operator
= Singular system of a compact operator
A singular system $(\sigma_j,u_j,v_j)$ for a compact operator $A:X\to Y$ has positive singular values $\sigma_j\to0$ and orthonormal vectors satisfying $Av_j=\sigma_j u_j$ and $A^*u_j=\sigma_jv_j$. It diagonalizes spectral regularization methods.