Eigenvalue & Eigenvector Calculator
Linear Algebra Calculator
Calculate eigenvalues and eigenvectors for 2x2 and 3x3 matrices with detailed solutions.
Matrix Input
What are Eigenvalues?
Eigenvalues (λ) and eigenvectors (v) satisfy the equation: Av = λv
A scalar that scales the eigenvector
A non-zero vector that only changes by a scalar factor when the matrix is applied
Features
- 2×2 and 3×3 matrix support
- Eigenvalue calculation
- Eigenvector calculation
- Trace calculation
- Determinant calculation
- Characteristic polynomial
- Normalized eigenvectors
- Quick example matrices
- Copy results
Properties
Sum of diagonal elements = sum of eigenvalues
Product of all eigenvalues
All eigenvalues are 1
Eigenvalues are diagonal entries
Note
2×2 Matrices: Exact calculation using quadratic formula
3×3 Matrices: Approximation using power iteration method (dominant eigenvalue)
Complex eigenvalues are not supported in this calculator
Use Cases
- Linear algebra homework
- Principal component analysis (PCA)
- Stability analysis
- Quantum mechanics
- Vibration analysis
- Graph theory
- Machine learning
- Differential equations
Applications
Real-World Applications:
Dimensionality reduction and feature extraction
Structural analysis and vibration modes
Quantum states and energy levels
3D transformations and rotations
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