Eigenvalues & Eigenvectors

Eigenvalues and eigenvectors for 2×2 and 3×3 matrices

det(A − λI) = λ² − 4λ + 3 = 0

Trace

Determinant

Symmetric matrix: every eigenvalue is real and eigenvectors of distinct eigenvalues are orthogonal.

Eigenvalues & eigenvectors

Eigenvalue λ = 3

Eigenvectors

Eigenvalue λ = 1

Eigenvectors

Any nonzero scalar multiple of an eigenvector is also an eigenvector.