Eigenvalues & Eigenvectors

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

Matrix A
det(A − λI) = λ² − 4λ + 3 = 0
Trace
4
Determinant
3

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

Eigenvalues & eigenvectors
Eigenvalue λ = 3
Eigenvectors
  • (1, 1)
Eigenvalue λ = 1
Eigenvectors
  • (1, -1)

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

Eigenvector directionsEach eigenvector direction drawn through the origin as a dashed line, with the unit eigenvector and its image stretched by the eigenvalue λ; the dashed unit circle is shown for scale.xyλ=3λ=1