Eigenvalue and Eigenvector Calculator

Find eigenvalues and unit eigenvectors of a 2x2 or 3x3 matrix from the characteristic polynomial det(A - λI) = 0.

Frequently Asked Questions

What is an eigenvalue?

A scalar λ such that A·v = λ·v for some nonzero vector v. It is how much the matrix scales vectors that lie along its eigenvector direction.

Is the eigenvector unique?

Only up to nonzero scaling. Any constant multiple of an eigenvector is still an eigenvector. The calculator returns the unit-length version.

Why does my 3x3 matrix have complex eigenvalues?

Real matrices can have complex conjugate pairs of eigenvalues when they include a rotation. This usually means the matrix is not diagonalizable over the reals.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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