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!

Homework Help: Linear Algebra- Quadratic form and change of basis

  1. Feb 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose that for each v = (x1, x1, ... xn) in Rn, q(v) = XTAX for the given matrix A. For the given basis B of Rn, find the expression for q(v) in terms of the coordiantes yi of v relative to B.

    a) A = [tex]


    B = {(1,0,1), (3, {\sqrt{2}}, 1), (3{\sqrt{2}}, -4, {\sqrt{2}}) [/tex]

    2. Relevant equations

    3. The attempt at a solution

    So I read the theorem about A wrt to B is PTAP where P is the change of basis matrix from B to E3.. so I can just get A wrt to B by doing that right? I transpose P and the multiply it out like that? And it should give me a diagonal matrix?

    But when I do that I get something really wrong? Like nothing is diagonal.
    Is it possible for the result to have a zero column and q(v) wrt to B will not have all the terms?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted