# non-zero vector

A non-zero vector in a vector space^{} $V$ is a vector that is not equal to
the zero vector in $V$.

If $\mathbf{u}$ is a non-zero vector in $V$ and $a$ is a scalar, i.e. an element of the field over which $V$ is defined, then the equation $a\mathbf{u}=\mathrm{\U0001d7ce}$ is possible only in the case $a=0$.

Title | non-zero vector |
---|---|

Canonical name | NonzeroVector |

Date of creation | 2013-12-01 16:50:29 |

Last modified on | 2013-12-01 16:50:29 |

Owner | matte (1858) |

Last modified by | pahio (2872) |

Numerical id | 6 |

Author | matte (2872) |

Entry type | Definition |

Classification | msc 15-00 |