solving difference equations with matrices
(35 minutes to learn)
Difference equations, such as the recurrence formula for the Fibonacci sequence, can be represented as powers of a matrix. If that matrix is diagonalizable, the eigenvalues and eigenvectors yield a closed form solution to the difference equation.
This concept has the prerequisites:
- diagonalization (Diagonalization is used to solve the difference equation.)
Core resources (read/watch one of the following)
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
→ Multivariable Mathematics
A textbook on linear algebra and multivariable calculus with proofs.
Location: Section 9.3, "Difference equations and ordinary differential equations," subsection 9.3.1, "Difference equations," pages 436-439
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location: Section 6.2, "Diagonalizing a matrix," subsection "Fibonacci numbers," pages 301-302
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