Matrix Eigenvectors Calculator
Compute eigenvectors for each eigenvalue of a 2×2 or 3×3 real matrix.
About Matrix Eigenvectors Calculator
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
Worked example
With the default values below, Matrix Eigenvectors Calculator returns Eigenvectors of λ = 3: [1, 1] λ = 1: [-1, 1]. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Matrix A (rows separated by newlines or semicolons; values by commas or spaces)
- 2 1 1 2
Results
- Eigenvectors
- λ = 3: [1, 1] λ = 1: [-1, 1]
- Eigenvalues Used
- 3, 1
Step by step
- 1Matrix A= 2 1 1 2
- 2Eigenvalues (real only)= 3, 1
- 3Eigenvectors (one per eigenvalue)= λ = 3: [1, 1] λ = 1: [-1, 1]
- 4Method= Null space of (A − λI) via RREF
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.