Eigenvalue and Eigenvector Calculator (2×2)
The Eigenvalue and Eigenvector Calculator finds the eigenvalues and eigenvectors of a 2×2 matrix by solving its characteristic equation. Enter the four matrix entries.
Formula
Solve det(A − λI) = 0: λ = (trace ± √(trace² − 4·det)) / 2
- Eigenvectors solve (A − λI)v = 0 for each eigenvalue.
- A negative discriminant gives complex-conjugate eigenvalues.
[[2,1],[1,2]]
Inputs
- a₁₁: 2
- a₁₂: 1
- a₂₁: 1
- a₂₂: 2
λ = 3 and 1, with eigenvectors (1, 1) and (1, −1).
Frequently asked questions
What is an eigenvector?
A non-zero vector whose direction is unchanged by the matrix; it is only scaled by its eigenvalue.