Linear Algebra › Section E · Eigenvalues and eigenvectors › Topic E.3
Diagonalization
Many matrices are diagonal matrices in disguise: change to a basis of eigenvectors and all that is left is a list of stretch factors. Writing a matrix this way makes its powers, and so its long-run behaviour, easy to compute.
In this topic
- Why diagonal matrices are easy
- The diagonalisation theorem
- Why the theorem works
- Worked example: a 2 × 2 matrix and its powers
- Distinct eigenvalues are enough
- Repeated eigenvalues
- Worked example: a repeated eigenvalue
- Powers and the long run
- Beyond diagonalisation
- Common mistakes to avoid
- Key takeaways
This topic is part of Wuanberri Pro. Checking your access…