Function Decomposition

The title of this chapter may seem a little odd. Why would we want to decompose a function? The word “decompose” is a bit formal. What we mean is that we’re going to break down a function into smaller, easier-to-understand bits. This is very similar to how we decomposed matrices in Chapter 3, using eigendecomposition and the singular value decomposition (SVD). The difference is that now, our mathematical object is a function, not a matrix. Function decomposition allows us to see how functions are made, and to see where their properties and characteristics come from. Function decomposition also allows us to do the reverse – that is, build up or compose a function from simple building blocks – and in doing so construct a function with properties and characteristics that are useful to us. This is a beneficial skill to have as a data scientist, where we often want to construct a function with specific characteristics as part of...