Linear Algebra › Section E · Eigenvalues and eigenvectors › Topic E.1
Eigenvectors and eigenvalues
A matrix pushes most vectors off their own line, but a few special directions are only stretched, shrunk or flipped. Those directions and their stretch factors are the key to understanding what a matrix does when it is applied again and again.
In this topic
- Directions a matrix leaves alone
- The definition
- Testing a vector
- Testing a scalar
- Eigenspaces
- Worked example: testing two candidate eigenvalues
- Worked example: a two-dimensional eigenspace
- Triangular matrices and the eigenvalue zero
- Different eigenvalues, independent eigenvectors
- Eigenvectors you can see
- Common mistakes to avoid
- Key takeaways
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