Physics I / Eigenvalues and Eigenvectors

Practice question · Put in order

Order the steps to find eigenvalues and eigenvectors.

Compute $\det(A - \lambda I) = 0$ (characteristic equation)
Solve for eigenvalues $\lambda$
Form A − $\lambda I$
For each $\lambda$ , solve (A − $\lambda I$ ) $v = 0$ for eigenvectors

Hints

The characteristic equation must be solved before any direction can be found.
Each eigenvector is found by solving a system for its own eigenvalue.

Show the answer

Form A − $\lambda I$
Compute $\det(A - \lambda I) = 0$ (characteristic equation)
Solve for eigenvalues $\lambda$
For each $\lambda$ , solve (A − $\lambda I$ ) $v = 0$ for eigenvectors

Why

First find the eigenvalues, then the corresponding eigenvectors.

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