Eigenvalues and Eigenvectors

Eigenvalues and eigenvectors play a prominent role in the study of ordinary differential equations and in the physical sciences. One example that always comes to mind is Quantum Mechanics, which depends heavily on eigenvectors and eigenvalues.

Eigenvalues and eigenvectors are especially helpful in the process of transforming a given matrix into a diagonal matrix, which is easy to work with.

The eigenvalue problem for a matrix can be defined as follows:

$Av_{n}=\lambda_{n} v_{n}$

where $\lambda_{n}$ is $n^{th}$ eigenvalue

and $v_{n}$ is $n^{th}$ eigenvector

Eigenvalues

To compute the eigenvalues, we use the eigvals method with the matrix as the input argument. It returns an ndarray with the eigenvalues of the input matrix.