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[parent] homogeneous linear problem (Definition)

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

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



"homogeneous linear problem" is owned by rmilson.
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See Also: linear equation

Other names:  homogeneous

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Cross-references: injective, kernel, solution, linear equation, linear mapping
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This is version 2 of homogeneous linear problem, born on 2002-02-22, modified 2007-03-27.
Object id is 2500, canonical name is HomogeneousLinearProblem.
Accessed 6869 times total.

Classification:
AMS MSC: 15A06 (Linear and multilinear algebra; matrix theory :: Linear equations)
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