Differential Equations › Section E · Systems of differential equations › Topic E.6
Complex eigenvalues
A real matrix can have complex eigenvalues, and when it does the solutions rotate. This topic turns one complex solution into two real ones, then reads the rotation, its speed and its growth or decay straight from the eigenvalue.
In this topic
- Where rotation comes from
- One complex solution gives two real ones
- Worked example: a centre
- Reading the centre
- Worked example: a stable spiral
- Reading the spiral
- Growth rate and frequency
- Common mistakes to avoid
- Key takeaways
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