Suppose you have a set of vectors v1 v2 v3, etc.(adsbygoogle = window.adsbygoogle || []).push({});

However large they are, suppose they span some area, which I think is typically represented by

Span {v1, v2, v3}

But I mean, if you're given these vectors, is there anything wrong with rearranging them? Because there's a theorem- that

"an indexed set S= {v1, v2... vp} of more than one vectors is linearly dependent if at least one vector is in a linear combination of the others."

So if S is linearly dependent, any vector in the set is a combination of the preceeding vectors?

Or did I read that wrong, and it just means a certain vector, possibly more than one is a lin comb of some other vectors?

However the theorem i'm reading seems to really detail that there's something special about "preceeding vectors". So if you have any set, is interchanging vectors allowed?

I feel like that there is nothing wrong with this. Is there some time when this is allowed and it isnt, maybe?

(I've just started linear algebra for a few weeks so I don't know any complex scenarios)

But it seems that this theorem suggests that there's something important to thepermutationof these vectors.

**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!

# Can you rearrange vectors in a set? And another misc questn.

Loading...

Similar Threads - rearrange vectors another | Date |
---|---|

I Understanding Hilbert Vector Spaces | Mar 2, 2018 |

I The vector triple product | Feb 15, 2018 |

Rearranging Equations | May 20, 2012 |

Rearranging redshift formula for v | Jun 23, 2011 |

Rearranging Formulae | Apr 14, 2007 |

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