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: Orthogonal Matrix

  1. Nov 28, 2006 #1
    Assume that [tex] I [/tex] is the [tex] 3\times 3 [/tex] identity matrix and [tex] a [/tex] is a non-zero column vector with 3 components. Show that:

    [tex] I - \frac{2}{| a |^{2}}aa^{T} [/tex] is an orthogonal matrix?

    My question is how can one take the determinant of [tex] a [/tex] if it is not a square matrix? Is there a flaw in this problem?

    Last edited: Nov 28, 2006
  2. jcsd
  3. Nov 28, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    I assume you are referring to the [tex] | a |^{2} [/tex] and I also assume that is the inner product (dot product) for the vector. It's just a normalization factor
  4. Nov 28, 2006 #3


    User Avatar
    Science Advisor

    Yes. |a| is not a "determinant", it is the length of the vector a.
  5. Nov 28, 2006 #4
    Remember that [itex]aa^{T} [/itex] does NOT equal [itex]a^{T}.a[/itex], the scalar product. Use matrix multiplication. You don't need to find the determinant of anything either.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook