Chapter 9: Advanced Concepts
In this chapter, we will go into some advanced linear algebra concepts. These will not come up all the time in quantum computing, but when they do, you should know what they are and where to find information about them. Almost all the topics are about decomposing a matrix. This becomes important in quantum computing because when we come up with a unitary transformation that we'd like to do on a quantum computer, we will only have certain unitary operators to use on it. Then, it becomes a question of which combination of available operators we should use so that we can perform our overall unitary transformation. Along the way, we will also look at important inequalities and how to represent functions that have matrices in them.
In this chapter, we are going to cover the following main topics:
- Gram-Schmidt
- Cauchy-Schwarz and triangle inequalities
- Spectral decomposition
- Singular value decomposition
- Polar decomposition
- Operator...
