# 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 |