Lecture1

Lecture

Definition

Given a square matrix A, a scalar λ is an eigenvalue if:

Av = λv

for some nonzero vector v. We find eigenvalues by solving:

det (A − λI) = 0

Example

For $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$, the characteristic polynomial is λ² − 4λ + 3 = 0, giving eigenvalues λ₁ = 3 and λ₂ = 1.