Eigenvalues λ satisfy det(A−λI) = 0. For a 2×2 matrix, this gives a quadratic; for 3×3, a cubic. Once eigenvalues are found, eigenvectors come from solving (A−λI)v = 0. Key: trace = sum of eigenvalues, determinant = product of eigenvalues.
How to Use
Enter a square matrix:
- Size: 2×2 or 3×3
- Values: Fill entries
- Result: Eigenvalues and eigenvectors
Properties
- Trace = λ₁ + λ₂ + ...
- Det = λ₁ × λ₂ × ...
- Symmetric → real eigenvalues
Applications
PCA (data science), Google PageRank, quantum states, stability analysis, vibration modes, facial recognition.
Step-by-Step Instructions
- 1Choose 2×2 or 3×3.
- 2Enter matrix values.
- 3View eigenvalues.
- 4Check eigenvectors.
- 5Verify trace and determinant.