Mathematics - Linear Algebra - Eigenvalues and eigenvectors - Finding Eigenvalues and Eigenvectors

10 steps: (1) Eigenvalue equation: Av = λv. 'A transforms v by just scaling it by λ.' (2) Rearrange: (A-λI)v = 0. For non-trivial v, det(A-λI) = 0. (3) This is the CHARACTERISTIC EQUATION. (4) Example: A=[[4,1],[2,3]]. (5) det([[4-λ,1],[2,3-λ]]) = (4-λ)(3-λ)-2 = λ²-7λ+10 = (λ-5)(λ-2) = 0. (6) Eigenv