Matrix Decomposition Demystified
In this article, we discuss the following:
- Eigen Decomposition
- Singular Value Decomposition
- Pseudo-inverse Matrix
These three subjects are related to each other.
Once we know how Eigen Decomposition works, we can understand how Singular Value Decomposition works. Once we know SVD, we can understand Psuedo-inverse Matrix.
We discuss the following topics in the order:
- Square Matrix
- Eigenvalue and Eigenvector
- Symmetric Matrix
- Eigen Decomposition
- Orthogonal Matrix
- Singular Value Decomposition
- PSeudo-inverse Matrix
Square Matrix
Eigen Decomposition works only with square matrices.
As a quick reminder, let’s have a look at what a square matrix is.
In square matrices, the number of rows and the number of columns are the same.
For example,
That was easy. Let’s continue to Eigenvalue and Eigenvector concepts.
