To find the eigenvectors $\mathbf X$ of a matrix $\mathbf A$, we construct the eigen equation
where $\lambda$ is the eigenvalue.
To make it seaier to understand, we rewrite it in the components form,
Mathematically speaking, it is straightforward to find the eigenvectors and eigenvalues.
Reconstruct $\mathbf A$
We can reconstruct $\mathbf A$ using the eigenvalues and eigenvectors.
First of all, we will construct a matrix of eigenvectors,
We also construct a diagonalized matrix $\mathbf \Lambda$
The original matrix $A$ is reconstrut by