Eigenvalues and Eigenvectors Calculator

Calculate eigenvalues and eigenvectors for square matrices with step-by-step explanations

• Linear Algebra Tool• Matrix Analysis• Educational Calculator• Free Online Tool
Matrix Input
Dimensions: 2 × 2 (Square Matrix)
Matrix Size:2

Enter matrix values

Results
Eigenvalues and eigenvectors calculation results

Enter matrix values and click "Calculate Eigenvalues" to see results

About Eigenvalues and Eigenvectors

Key Concepts:

  • • Eigenvalue λ: A scalar that satisfies Av = λv
  • • Eigenvector v: A non-zero vector that doesn't change direction
  • • Characteristic equation: det(A - λI) = 0
  • • Only square matrices have eigenvalues

Applications:

  • • Principal Component Analysis (PCA)
  • • Quantum mechanics
  • • Stability analysis
  • • Google PageRank algorithm