# Diagnolize Matrices

## #Linear Algebra

Given a matrix $\mathbf A$, it is diagonalized using its eigenvectors.

- Find the eigenvectors $\mathbf x_i$ of the matrix $\mathbf A$; If we find degerations, the matrix is not diagonalizable.
- Construct a matrix $\mathbf S = \begin{pmatrix} \mathbf x_1 & \mathbf x_2 & \cdots & \mathbf x_n \end{pmatrix}$;
- The matrix $\mathbf A$ is diagonalize using $\mathbf S^{-1} \mathbf A \mathbf S = \mathbf {A_D}$

Published:
by Lei Ma;

Lei Ma (2020). 'Diagnolize Matrices', Datumorphism, 03 April. Available at: https://datumorphism.leima.is/cards/math/diagonalize-matrix/.

**Current Ref:**

- cards/math/diagonalize-matrix.md