Eigenvector

An eigenvector is a non-zero vector $u$ that changes at most by a constant factor when the linear transform (multiply with matrix) is applied to it. The factor that it changes by is denoted with $\lambda$ and is called the eigenvalue.

How to find Eigenvectors?

1. First find the eigenvalues by solving the characteristic-polynomial set to 0
2. Find basic solutions by solving $(\lambda I-A)X=0$