1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear algebra

  1. Jan 29, 2009 #1
    i am given a subspace of R4 W={(a b c d)} and know a+c=0 c-2d=0, and am asked to find a basis for W,
    i wrote (-2 0 2 1)(0 1 0 0),
    now i am asked to find the missing vectors so that the new basis will be a basis for R4. to find this i need vectors that are independant and are the basis for R4-W???? how can i do this??
    just a guess would be (-2 0 2 1)(0 1 0 0)(0 0 1 0)(0 0 0 1) but thats just because i know that those four would cover the whole space and are independant. what is the mathematical way of solving this?
  2. jcsd
  3. Jan 29, 2009 #2


    Staff: Mentor

    Gram-Schmidt process --http://en.wikipedia.org/wiki/Gram_schmidt
  4. Jan 29, 2009 #3
    another question, not related,
    is it possible for 2 seperate basises of a subspace to be linearly independant of one another, or do they always need to be dependant
  5. Jan 29, 2009 #4


    Staff: Mentor

    I don't think it's meaningful to talk about one basis being independent of another. For linear independence/dependence, we're always talking about a collection of vectors.

    Suppose v1, v2, ... , vn are a basis for a subspace W and u1, u2, ..., un are another basis for W. The set of vectors {v1, v2, ..., vn, u1} has to be a linearly dependent set, meaning that u1 has to be a linear combination of v1, v2, ... , vn.

    A basis for a subspace W is the largest set of vectors that a) is linearly independent, and b) spans W. If you add any vector to this basis, the added vector must be a linear combination of the original basis vectors.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Linear algebra
  1. Linear algebra (Replies: 3)

  2. Linear Algebra (Replies: 5)

  3. Linear Algebra (Replies: 1)