Results 1 to 2 of 2

Math Help - Wedge product and vectors

  1. #1
    Member
    Joined
    Oct 2010
    Posts
    131

    Wedge product and vectors

    Hello,

    i want to proof this claim:

    Let V be a finite vector space.
    v_1,..,v_n are not linearly indipendent <=> v_1 \wedge...\wedge v_n=0.

    One direction(=>) wasn't so difficult. But i have problems with the other direction.
    So we have 0=v_1 \wedge...\wedge v_n=\sum_{\sigma \in S_n}sgn(\sigma)(v_{\sigma(1)}\otimes...\otimes v_{\sigma(n)}).

    Can you see, why they have to be linearly dependent?

    Regards
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    May 2010
    Posts
    95
    Quote Originally Posted by Sogan View Post
    Hello,

    i want to proof this claim:

    Let V be a finite vector space.
    v_1,..,v_n are not linearly indipendent <=> v_1 \wedge...\wedge v_n=0.

    One direction(=>) wasn't so difficult. But i have problems with the other direction.
    So we have 0=v_1 \wedge...\wedge v_n=\sum_{\sigma \in S_n}sgn(\sigma)(v_{\sigma(1)}\otimes...\otimes v_{\sigma(n)}).

    Can you see, why they have to be linearly dependent?

    Regards
    Just wondering, how do you derive this? v_1 \wedge...\wedge v_n=\sum_{\sigma \in S_n}sgn(\sigma)(v_{\sigma(1)}\otimes...\otimes v_{\sigma(n)})?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. differential form and wedge product
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: January 24th 2011, 11:37 PM
  2. vectors and dot product in 3-d
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 25th 2009, 04:52 PM
  3. Replies: 1
    Last Post: May 14th 2008, 12:31 PM
  4. [SOLVED] Question on wedge product
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 20th 2008, 03:47 AM
  5. Product Dot Vectors
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 21st 2008, 01:37 PM

Search Tags


/mathhelpforum @mathhelpforum