eigenvectors

eigenvalue

Given a square matrix A, an eigenvector is a direction that doesn’t change when you apply A to it, only scales.

$A\overrightarrow{v}=\lambda \overrightarrow{v}$ $\lambda$ is the eigenvalue.

computation

$A\overrightarrow{v}=\lambda \overrightarrow{v}\to (A-\lambda I)\overrightarrow{v}=0$

• we want a non-zero v, so we must have $det(A-\lambda I=0)$

compute determinant to get quadratic equation in lambda - solve for eigenvalues

for each eigenvalue, solve original equation to get eigenvectors