homogeneous linear problem

Let L:UV be a linear mapping. A linear equation is called homogeneousPlanetmathPlanetmathPlanetmath if it has the form


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 injectivePlanetmathPlanetmath.

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