Eigenvector Calculator

Enter a 2×2 or 3×3 matrix — one row per line, entries separated by spaces or commas — to find a unit eigenvector for each real eigenvalue.

Matrix A

Eigenvalues (λ) —

Eigenvectors (v) —

Frequently Asked Questions

What is an eigenvector?

An eigenvector v of a square matrix A is a non-zero vector whose direction is unchanged by A: Av = λv, where the scalar λ is the matching eigenvalue. A stretches v by the factor λ. For [[2, 0], [0, 3]] the eigenvectors are the axes (1, 0) and (0, 1).

How are eigenvectors calculated?

For each eigenvalue λ, solve (A − λI)v = 0. That homogeneous system is singular, so it has a non-zero solution; its null space is the eigenvector direction. This tool row-reduces A − λI and returns a unit vector. For [[4, 1], [2, 3]] the eigenvalue 5 gives v ∝ (1, 1) and 2 gives v ∝ (1, −2).

Can eigenvectors be complex?

A real matrix can have complex eigenvalues in conjugate pairs, and those have complex eigenvectors with no real direction. This tool returns real eigenvectors and notes when a complex pair is present. A real symmetric matrix always has a full set of real, orthogonal eigenvectors.

Is my data sent anywhere?

Your figures stay on your device when you use the eigenvector calculator. The eigenvector calculator works in the browser using JavaScript, with no server round-trip at any point, so your matrix entries are never transmitted. Nothing is logged, stored or shared with a third party. That also means the tool keeps working offline.

Eigenvector Calculator

Frequently Asked Questions

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