Eigenvalues and Eigenvectors (AQA A-Level Further Maths): Flashcards

$\mathbf{Ax} = \lambda\mathbf{x}$

Non-zero vector maintaining direction under transformation

Scaling factor ($\lambda$) for eigenvector

$\det(\mathbf{A} - \lambda\mathbf{I}) = 0$

Every matrix satisfies its own characteristic equation

$\mathbf{M} = \mathbf{PDP}^{-1}$

$\mathbf{A}^n = \mathbf{PD}^n\mathbf{P}^{-1}$

Raise each diagonal element to power $n$

$\lambda = 1$

Repeated eigenvalue