I may have a bad day, or not enough coffee yet.(adsbygoogle = window.adsbygoogle || []).push({});

So,

"If A is a nonempty subset of a vector space V, then the set

L(A) of all linear combinations of the vectors in A is a subspace, and it is

the smallest subspace of V which includes the set A.

If A is infinite, we obviously can't use a single finite listing. However, the

sum of two linear combinations of elements of A is

clearly a finite sum of scalars times elements of A."

Question:

If A is infinite, how can the sum of its linear combinations be finite (even choosing a finite sum of scalars)?

Thank you.

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

Join Physics Forums Today!

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

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

# Smallest subspace of a vector space

Loading...

Similar Threads - Smallest subspace vector | Date |
---|---|

I Subspace question | Feb 5, 2017 |

The pure-point subspace of a Hilbert space is closed | Aug 24, 2013 |

Graphs of Continuous Functions and the Subspace Topology | Mar 22, 2013 |

Are Quotients by Homeomorphic Subspaces Homeomorphic? | Nov 19, 2012 |

The usual topology is the smallest topology containing the upper and lower topology | Oct 2, 2011 |

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