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!

Matrix of a quadratic form

  1. Nov 7, 2011 #1
    1. The problem statement, all variables and given/known data
    Consider the quadratic form
    q(v) = x12 + 5x22 + 11x32 + 4x1x2 + 6x1x3 + 14x23

    Relative to the standard basis of R3 find the symmetric matrix A associated with q.

    3. The attempt at a solution
    In the standard basis, I'll use
    e1 = [1,0,0]
    e2 = [0,1,0]
    e3 = [0,0,1]

    if it were in R2, I would say [aij] = q(ei,ej) but how do I do this in R3? and I only have 3 variables, so I have to only use one vector, but which entry in the matrix does each one represent?
    How do I determine which vectors to use for with entries.

    *edit* I'll just specify, if I wanted to find [a11] I could just use q(e1), but what about [a21] for example?
     
    Last edited: Nov 7, 2011
  2. jcsd
  3. Nov 7, 2011 #2
    my book does not explain anything... Can anyone recommend a good one?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Matrix of a quadratic form
  1. Quadratic Forms (Replies: 0)

  2. Quadratic forms (Replies: 3)

Loading...