Why do we want to decompose a function?
Decomposing a function means breaking it down into its component parts. The reason for doing so is the same as why we wanted to decompose a matrix in Chapter 3 using the eigendecomposition or using the SVD – to break it down into simpler parts. By simpler, we mean breaking a function down into a sum of functions that are easier to understand, have nicer properties, and behave in ways we understand when we transform them.
What is a decomposition of a function?
We have already answered this question to some degree. Decomposing a function, 
, means writing that function as a sum of other functions. In math, that means we write the following:
Eq. 1
The number of functions, 
, that we decompose, 
, into could be finite or infinite. It depends on what we want to do with the decomposition on the right-hand side of Eq. 1.
We also haven’t said what the component functions, 
, are yet. Again, the choice of components, 
, will...
