# solving difference equations with matrices

(35 minutes to learn)

## Summary

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.

## Context

This concept has the prerequisites:

- diagonalization (Diagonalization is used to solve the difference equation.)

## Core resources (read/watch one of the following)

## -Free-

→ MIT Open Courseware: Linear Algebra (2011)

Videos for an introductory linear algebra course focusing on numerical methods.

## -Paid-

→ 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

## See also

-No Additional Notes-