Mastering Numerical Computing with NumPy

Eigenvalue decomposition

Eigenvalue decomposition is also a decomposition technique that applies to square matrices. When you decompose a square matrix (M) using eigenvalue decomposition, you will get three matrices. One of these matrices (Q) contains eigenvectors in columns, another matrix (L) contains eigenvalues in its diagonal, and the last matrix is a transpose of the matrix of eigenvectors (Q^-1).

This can be summed up in the following formula:

M=QVQ^-1

Eigenvalue decomposition will give you the matrices' eigenvalues and eigenvectors.

The following is an illustration of eigenvalue decomposition:

Let's see how it's implemented using numpy ...