CSCI 8945 · In-class tool
Eigenvalues & eigenvectors of a 2×2 matrix
Adjust the matrix M and rotate the input vector v with the sliders. The red and orange lines mark the eigenvector directions — the only two orientations where the transformed vector Mv stays parallel to v, just scaled by an eigenvalue.
Matrix M
M =
2.01.0
1.02.0
trace = 4.00
det = 3.00
det = 3.00
Input vector v
Transformation view
v = input · Mv = output · —— eigenvector lines (dashed)
Eigendecomposition
Mv = λv ⇒ v is an eigenvector with eigenvalue λ.
Eigenvalues & eigenvectors
—
Current vectors
v = —
Mv = —
|Mv| / |v| = — angle(v, Mv) = —
Mv = —
|Mv| / |v| = — angle(v, Mv) = —
Drag the θ slider to rotate v. When v aligns with an eigenvector line, Mv becomes parallel to v.