Compact operators and singular value decomposition
Tailen Hsing, Randall L. Eubank · Wiley series in probability and statistics · 2015
In this chapter we continue the discussion of operators that was begun in Chapter 3. In doing so we will narrow our focus to the special case of compact operators. When working with Hilbert spaces, this type of operator can be approximated by finite-dimensional operators and, as a result, exhibits similar properties to those we are familiar with from the study of matrices. A key result is the singular value decomposition, which characterizes compact operators. We also consider the special cases of Hilbert-Schmidt, trace class and integral operators.