---
tag: 0YA7X86K05
kind: concept
name: Characteristic polynomial of a linear recurrence
msc: [39A06]
sources:
  - url: https://en.wikipedia.org/wiki/Linear_recurrence_with_constant_coefficients
    locator: Characteristic polynomial and roots
---

## Summary

The characteristic polynomial of a linear recurrence encodes its coefficients as a polynomial. Its roots give the geometric solutions, and they lead to closed formulas for all solutions. The node [[characteristic polynomial of a linear recurrence|0BWDJGQYST]] gives the precise definition.