Linear Algebra
Eigenvalue Calculator
Inspect the eigenvalues, eigenvectors, trace, and determinant of a 2×2 matrix in one panel.
eigenvalueeigenvectorcharacteristic polynomial
Eigenvalues (2×2)
Compute eigenvalues and normalized eigenvectors for a 2×2 matrix.
Trace
7
Determinant
10
Eigenvalues
5, 2
Eigenvector λ₁
0.707107 -0.707107
Eigenvector λ₂
-0.894427 -0.447214
Characteristic equation
λ² − (a + d)λ + (ad − bc) = 0
Eigenvalues solve the characteristic polynomial. For each eigenvalue, the calculator returns a normalized eigenvector.
How to use
- Enter a 2×2 matrix with two numbers per row.
- Submit to compute eigenvalues λ₁ and λ₂ along with representative eigenvectors.
- Review supporting information like trace and determinant.
Example
Input: Matrix = [[4,1],[2,3]]
Output: Eigenvalues ≈ 5.5616 and 1.4384 with normalized eigenvectors.
FAQ & notes
Does it handle complex eigenvalues?
When the discriminant is negative the calculator reports the repeated real component. Complex visualization is planned for a future update.
Can I analyse larger matrices?
This tool focuses on 2×2 matrices for clarity. Use the polynomial solver for higher-degree characteristic equations.