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!

Standard Matrix of Linear Transformation

  1. Apr 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Let T: R3-->R3, defined by T(x)= a x x
    Give the standard matrix A of T, and explain why A is skew-symmetric.

    2. Relevant equations

    They define u x v as

    u x v=(det [u2 u3/ v2 v3], det [u3 u1 /v3 v1], det [u1 u2/ v1 v2])

    For any vectors u,v,w in R3, w.(uxv)=D(w,u,v)

    Ax.y=x.A^Ty

    3. The attempt at a solution

    I'm not really sure how to find a standard matrix for this, so I haven't made much progress.
     
  2. jcsd
  3. Apr 3, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    If [itex]\textbf{y}= \textbf{a} \times \textbf{x}, [/itex] write [itex] y_1, y_2 \text{ and } y_3[/itex] in terms of [itex] x_1, x_2 \text{ and } x_3.[/itex]

    RGV
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook