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.