Spectrum decomposition can be regarded as the generalizations of the following fact that: Every Hermitian matrix $A$ can be decomposed into $A=U^{*}\Lambda U$,where $U$ is a unitary matrix

Singular vector decomposition can be expressed as Every Matrix $A_{mn}$ can be decomposed in to $A=U\Lambda V^{*}$, where $U$,and $V$ are unitary matrices. Does it can be extended in to decompostion of linear operators on Hilbert Space. ?

I searched the internet and several traditional books about the topic "Singular Vector Decomposition into Hilbert space", However, to my disappointment, I find no similar conclusion. Thanks for your help.

iscovered in functional analysis textbooks; and so I am voting to close this question. – Yemon Choi Apr 9 '11 at 6:06