# Eigenvalue-Eigenvector

06-27-2022 || 01:18
Tags: #linear-algebra

# eigenvalue-eigenvector

For any square matrix, the eigenvalue $\lambda$ and the eigenvector $\textbf{x}$ are formulated as,

$$Ax = \lambda x ; x \ne 0$$
Every eigenvalue $\lambda$ has a corresponding eigenvector $x$

To find eigenvalue and vecotor we need to solve this equation with determinant,
$$determinant(A - \lambda I) = 0$$
That will give us the eigenvalue $\lambda$, and using those we can get the corresponding eigenvector $x$