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

Every eigenvalue $\lambda$ has a corresponding eigenvector $x$

To find eigenvalue and vector, we need to solve this equation with determinant,

That will give us the eigenvalue $\lambda$, and using those we can get the corresponding eigenvector $x$

References

• Deep Learning by Ian Goodfellow
• Tutorial 1