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: Quick Linear Algebra notation question

  1. Feb 24, 2010 #1
    For transformations, what exactly does T(x) mean?

    Does it mean T is the transformation matrix multiplied by a vector?

    How about T(x1, x2) ?
     
  2. jcsd
  3. Feb 24, 2010 #2
    [tex]T(x)[/tex] (or simply [tex]Tx[/tex]) means the result of applying the transformation [tex]T[/tex] to the vector [tex]x[/tex]. If you have the coordinate representations of these objects, i.e., the matrix of [tex]T[/tex] and the coordinates of the vector [tex]x[/tex], then the coordinates of the vector [tex]Tx[/tex] are indeed given by multiplying the matrix of [tex]T[/tex] by the coordinate vector of [tex]x[/tex], in that order.

    If [tex]T[/tex] happens to be a transformation whose domain space is two-dimensional, then [tex]T(x_1, x_2)[/tex] probably means the result of applying [tex]T[/tex] to the vector [tex](x_1, x_2)[/tex] where [tex]x_1, x_2[/tex] are numbers. If the domain space of [tex]T[/tex] is other than two-dimensional, there is no obvious candidate for the meaning of [tex]T(x_1, x_2)[/tex].
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook