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Homework Help: Vector notation

  1. Apr 17, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi guys

    If I have a vector v, then is it correct notation to write

    [tex]
    \mathbf v =
    \left( {\begin{array}{*{20}c}
    {v_1 } \\
    {v_2 } \\
    \end{array}} \right) = (v_1,v_2)^T,
    [/tex]

    where T is the transpose?
     
  2. jcsd
  3. Apr 17, 2010 #2
    Yes. Although you can write a vector as either a row or a column, the usual convention is to treat the column form as more basic:

    [tex]x = \begin{pmatrix} x_1\\ x_2 \end{pmatrix}[/tex]

    [tex]x^T = \begin{pmatrix}x_1 & x_2 \end{pmatrix}[/tex]

    so that the dot product [itex]\textbf{x} \cdot \textbf{y}[/itex] is usually expressed in matrix form as

    [tex]x^T y = \begin{pmatrix}x_1 & x_2 \end{pmatrix} \begin{pmatrix} y_1 \\ y_2 \end{pmatrix}[/tex]
     
  4. Apr 17, 2010 #3
    Thanks!
     
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