Differential Equations › Section E · Systems of differential equations › Topic E.1
Review: matrices, vectors, and eigenvalues
Every method in this section turns a system of differential equations into a question about a matrix. This review gathers the linear algebra you will lean on: solving linear systems, matrix arithmetic, determinants, inverses, independence and, above all, eigenvalues and eigenvectors.
In this topic
- Why matrices, and why now
- Solving linear systems by row reduction
- Worked example: a three-by-three system
- Matrix arithmetic
- Determinants, inverses and independence
- Eigenvalues and eigenvectors
- Worked example: two real eigenvalues
- Multiplicity and complex eigenvalues
- Worked example: complex eigenvalues
- Common mistakes to avoid
- Key takeaways
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