Eigenvalues and Eigenvectors
Eigenvalues and eigenvectors of a matrix through the characteristic polynomial, step by step.
Elements with spaces, rows with semicolons: 2 1; 1 2. Fractions as 1/2.
This calculator finds the eigenvalues and eigenvectors of a matrix through the characteristic polynomial.
- Write det(A − λE) = 0 and find its roots.
- For each root solve the system (A − λE)v = 0.
Example. For the matrix 2 1; 1 2 the polynomial is λ² − 4λ + 3, the eigenvalues are 1 and 3, the vectors are (−1, 1) and (1, 1).
Rational eigenvalues are exact, others are approximate and marked with ≈.
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