# homogeneous linear problem

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

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

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 HomogeneousLinearProblem 2013-03-22 12:26:03 2013-03-22 12:26:03 rmilson (146) rmilson (146) 5 rmilson (146) Definition msc 15A06 homogeneous LinearProblem