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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].
     
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