Linear Algebra › Section E · Eigenvalues and eigenvectors › Topic E.2
The characteristic equation
Testing one guess at a time is no way to find eigenvalues. A single determinant turns the search into solving a polynomial equation, and the same polynomial explains why the trace and determinant are tied to the eigenvalues.
In this topic
- From guessing to solving
- The characteristic polynomial
- The 2 × 2 shortcut
- Worked example: a 2 × 2 matrix
- Multiplicities
- Worked example: a 3 × 3 matrix
- Trace and determinant as checks
- Similar matrices
- How eigenvalues are computed in practice
- Common mistakes to avoid
- Key takeaways
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