Linear Algebra › Section D · Vector spaces › Topic D.8
Difference equations
Many quantities change in steps: a savings balance month by month, a population year by year, a sampled sound signal sample by sample. Linear difference equations describe such step-by-step change, and the ideas of subspace, basis and dimension tell you exactly what their solutions look like.
In this topic
- Signals and step-by-step change
- Linear difference equations
- Trying powers: the auxiliary equation
- Dimension of the solution space
- Testing independence: the Casorati matrix
- Worked example: a second-order equation
- Nonhomogeneous equations
- Worked example: a growing savings account
- Rewriting as a first-order system
- Common mistakes to avoid
- Key takeaways
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