Matrix Eigenvectors Calculator
Compute eigenvectors for each eigenvalue of a 2×2 or 3×3 real matrix.
Inputs
Eigenvectors
λ = 3: [1, 1] λ = 1: [-1, 1]
Eigenvalues Used
3, 1
Step by step
Matrix A
= 2 1 1 2
Eigenvalues (real only)
= 3, 1
Eigenvectors (one per eigenvalue)
= λ = 3: [1, 1] λ = 1: [-1, 1]
Method
= Null space of (A − λI) via RREF
How it works
An eigenvector v corresponding to eigenvalue λ satisfies (A − λI)v = 0. This calculator finds the null space of (A − λI) by row-reducing to RREF and reading off the free variables. Supported for 2×2 and 3×3 real matrices with real eigenvalues.
Formula
Eigenvector Equation
(A − λI)v = 0
- A
- Matrix
- λ
- Eigenvalue
- v
- Eigenvector
- I
- Identity
Frequently Asked Questions
Are eigenvectors unique?
No. Any scalar multiple of an eigenvector is also an eigenvector. This calculator returns one representative vector per eigenvalue, not normalised.
What if eigenvalues are complex?
This calculator only computes eigenvectors for real eigenvalues. Complex eigenvectors of real matrices are not currently supported.