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Eigenvalue & Eigenvector Calculator

Compute eigenvalues by solving the characteristic polynomial , then find corresponding eigenvectors by null-space computation.

Input Matrix

×3

Examples

Result

Enter a square matrix and click Find Eigenvalues

Characteristic Polynomial

The eigenvalues are the roots of . For 2×2 and 3×3, this gives quadratic and cubic equations solvable in closed form.

Eigenvectors

For each eigenvalue , the eigenvectors span the null space of . We find them by row-reducing to RREF.

Diagonalization

If has linearly independent eigenvectors, then where is the diagonal matrix of eigenvalues.