Diagonalize Matrix Calculator
The diagonalize matrix calculator is an easy-to-use tool for whenever you want to find the diagonalization of a 2x2 or 3x3 matrix.
Eigenvalues8.87298335, 1.12701665all real
Trace10equals the sum of the eigenvalues
Determinant10equals the product of the eigenvalues
Rank2
Sum of eigenvalues10
Product of eigenvalues10
Your matrix
| 4 | 7 |
| 2 | 6 |
The method
solve det(A − λI) = 0 for the eigenvalues λ
What an eigenvalue is
An eigenvector is a direction the matrix does not turn — it only stretches it. The eigenvalue is how much: Av = λv. Complex eigenvalues mean no real direction survives unturned, which is the signature of a rotation.
Two useful checks: the eigenvalues always sum to the trace and multiply to the determinant. Both are shown above.