Maths & numbers
2 × 2 eigenvalue calculator
Find real or complex-conjugate eigenvalues of a real 2 × 2 matrix.
A clear answer. Here’s how.
Solves the characteristic quadratic using matrix trace and determinant. Negative discriminants return conjugate complex values; repeated eigenvalues are repeated in the result. Uses floating-point arithmetic and does not compute eigenvectors or infer diagonalizability. For widely separated eigenvalues, subtraction can lose relative accuracy in the smaller root.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Matrix: one row per line
2, 1 1, 2
Example result
| Eigenvalue | Real part | Imaginary part |
|---|---|---|
| 1 | 3 | 0 |
| 2 | 1 | 0 |
Characteristic equation λ² − trace(A)λ + det(A)=0. Repeated eigenvalues do not imply two independent eigenvectors.