Eigenvalue Calculator
Calculate eigenvalues and eigenvectors of a 2x2 matrix.
Enter 2x2 Matrix
Characteristic Polynomial
det(A - lambda*I) = 0
lambda^2 - 7*lambda + 10 = 0
Matrix Properties
Trace (sum of eigenvalues)7.0000
Determinant (product of eigenvalues)10.0000
Discriminant9.0000
Eigenvalues
lambda1 = 5.000000
lambda2 = 2.000000
Eigenvectors (Normalized)
v1 (for lambda1 = 5.0000)
[0.8944, 0.4472]
v2 (for lambda2 = 2.0000)
[0.7071, -0.7071]
Type
Real
Distinct
Yes
Understanding Eigenvalues
- Eigenvalues represent scaling factors along eigenvector directions
- Sum of eigenvalues = Trace of matrix
- Product of eigenvalues = Determinant of matrix
- Complex eigenvalues indicate rotation