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University Math Lab: Systems & Structures FREE
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Eigenvalues & Eigenvectors
Learning Objectives
- Find eigenvalues
- Calculate eigenvectors
- Apply to transformations
Key Concepts
Eigenvalue
Scalar λ where Av = λv
Eigenvector
Non-zero vector v where Av = λv
Theory
**Finding Eigenvalues:**
1. Form det(A - λI) = 0
2. Solve characteristic polynomial
**Finding Eigenvectors:**
1. For each λ, solve (A - λI)v = 0
2. Find null space of (A - λI)
**Significance:** Eigenvectors don't change direction under transformation.
Examples
Find eigenvalues of [[2,1],[1,2]]
Solution: det = (2-λ)² - 1 = 0 → λ = 3, 1
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Knowledge Check
Test your understanding of The Eigen-Finder!