Mathematics is the foundation for many areas of science and engineering, and it is not uncommon for these applications to require the manipulation of large matrices. Though these applications are not mathematics, they use mathematics in everything they do and the methods to manipulate matrices are certainly mathematical. For this reason, I feel we should tour many methods used to manipulate matrices into any usable form. For the most part, we can divide the mathematical matrix methods into the following categories:
- Diagonalization / Finding the Eigenvalues
- Creating upper and lower diagonal matrices
- Solving systems of Equations
There are certainly more methods out there, so don't be offended if I have failed to list one of your favorite types of algorithms. We'll be filling more in as we go along!