Recently, I have been asked at least three times about resources for learning spectral techniques. Three is my threshold that warrants a short blog post 🙂

First, what are spectral techniques? It is a set of mathematical methods and tools that involve the analysis of the eigenvalues and eigenvectors of matrices associated with a given mathematical or data structure. Example of such data structures could be the adjacency matrix of a graph or the unitary matrix representing common quantum logic gates.

The use of spectral techniques are generally popular within fields (e.g., math, physics) that deal with data decompositions or linear transformations. Here are some resources (in mostly random order) for learning about spectral techniques:

1. NetworkX: A python playground for network analysis in Python.
2. The book on “Spectral Graph Theory” by Fan R. K. Chung which covers the mathematical basics of spectral graph theory.
3. The reference ”Spectral and Algebraic Graph Theory” by Daniel A. Spielman which contains background material and applications of spectral graph theory. It also has some accompanying code to further reinforce understanding! This is a huge plus.