Mr. Integral
Math notes/Linear Algebra/Eigenvalues and Dynamics

Eigenvalues and Eigenspaces — Cheat sheet

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Core rule

Av=λv, v≠0;Av=\lambda v,\ v\ne0; det⁡(A−λI)=0;\det(A-\lambda I)=0; Eλ=N(A−λI).E_\lambda=N(A-\lambda I).

Watch for

An eigenvalue may be zero, but an eigenvector may not. Find the null space for each eigenvalue.