homogeneous linear problem

Let $L:U\to V$ be a linear mapping. A linear equation is called homogeneous if it has the form

$$L(u)=0,u\in U.$$

A homogeneous linear problem always has a trivial solution, namely $u=0$. The key issue in homogeneous problems is, therefore, the question of the existence of non-trivial solutions, i.e. whether or not the kernel of $L$ is trivial, or equivalently, whether or not $L$ is injective.

Title	homogeneous linear problem
Canonical name	HomogeneousLinearProblem
Date of creation	2013-03-22 12:26:03
Last modified on	2013-03-22 12:26:03
Owner	rmilson (146)
Last modified by	rmilson (146)
Numerical id	5
Author	rmilson (146)
Entry type	Definition
Classification	msc 15A06
Synonym	homogeneous
Related topic	LinearProblem