Matrix Eigenvector Calculator

Use our free matrix eigenvector calculator to find the eigenvectors of 2×2 and 3×3 matrices for each real eigenvalue, solving (A − λI)v = 0.

Math

Matrix (2×2 or 3×3)

Formula

Eigenvectors v for eigenvalue λ satisfy (A − λI)v = 0. For each real eigenvalue, the calculator solves the homogeneous linear system to find a basis eigenvector (normalized).

(A − λI)v = 0 for each eigenvalue λ

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter a 2×2 or 3×3 square matrix.
2Click Calculate to find eigenvectors for each real eigenvalue.

Examples

2×2: [[4,1],[2,3]]

1.λ=5: solve [[−1,1],[2,−2]]v=0 → v ≈ [0.707,0.707]
2.λ=2: solve [[2,1],[2,1]]v=0 → v ≈ [−0.447,0.894]

Result: 0.707

Diagonal [[2,0],[0,3]]

1.λ=2: v=[1,0]
2.λ=3: v=[0,1]

Result: 1

Frequently Asked Questions

Non-zero vectors v such that Av = λv.

Solve (A − λI)v = 0 using Gaussian elimination.

Up to scaling — any multiple is also an eigenvector.

Compute eigenvectors for each distinct eigenvalue.

Eigenvectors are normalized to unit length.

Related Calculators

Matrix Eigenvalue Calculator Matrix Determinant Calculator Matrix Calculator Matrix Rank Calculator Percentage Calculator Basic Calculator

CalculateMe Team

Last updated: 2026-07-14

Matrix Eigenvector Calculator

Formula

How It Works

Examples

2×2: [[4,1],[2,3]]

Diagonal [[2,0],[0,3]]

Frequently Asked Questions

What are eigenvectors?

How are they computed?

Are eigenvectors unique?

What if eigenvalues repeat?

Normalized?

Related Calculators

Matrix Eigenvector Calculator

Formula

How It Works

Examples

2×2: [[4,1],[2,3]]

Diagonal [[2,0],[0,3]]

Frequently Asked Questions

What are eigenvectors?

How are they computed?

Are eigenvectors unique?

What if eigenvalues repeat?

Normalized?

Related Calculators