---
tag: 0469V0EN5N
kind: concept
name: Homogeneous linear system with constant coefficients
msc: [34A30]
sources:
  - url: https://en.wikipedia.org/wiki/Matrix_differential_equation
    locator: Solution in matrix form
---

## Summary

A homogeneous linear system with constant coefficients is a system $x' = A x$ with a constant square matrix $A$.
Its solutions are given by the matrix exponential, and the eigenvalues of $A$ control their behaviour. See the [[definition|0VJF99CZ0Z]].