In the book it states that the span of the empty set is the trivial set because a linear combination of no vectors is said to be the 0 vector. I really don't know how they came up with at? Is it just defined to be like that?(adsbygoogle = window.adsbygoogle || []).push({});

After doing some research, I figured that since the empty set is a subset of every set and that the zero vector is a subspace of every vector space that means that the span({})={0}?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Empty set as a vector space?

Loading...

Similar Threads - Empty vector space | Date |
---|---|

Structure of a Matrix With Empty Null Space | Jan 6, 2015 |

The exclusion of empty substructures | Dec 8, 2014 |

EMPTY subset of a ring | Apr 1, 2007 |

Empty Set and Vector Space | Aug 3, 2005 |

Intersection of disjoint SETS is empty | Sep 1, 2004 |

**Physics Forums - The Fusion of Science and Community**