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A question on vector placing

  1. Feb 29, 2008 #1
    in previous question
    i was tald that in the proccess of building the transformation matrix

    i should have put the vectors of the new base as columns and not as rows

    in what cases and in what formes i put them as rows??
    in what cases and in what formes i put them as columns??
  2. jcsd
  3. Mar 1, 2008 #2
    Think about transposition...


  4. Mar 1, 2008 #3


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    Homework Helper

    Also, you can always check by applying the transformation matrix to one of your basis elements. If you want A to transform the vector v into the vector w, you can check that indeed
    Av = w
    A-1 w = v.

    For example, if you write down a general matrix
    [tex]A = \begin{pmatrix} a_{11} & a_{12} & \cdots \\ a_{21} & a_{22} & \cdots \\ \vdots & \ddots & \cdots \end{pmatrix}[/tex]
    you can apply it to the (old) basis vector
    [tex]e_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \\ \vdots \end{pmatrix}[/tex]
    and just do the multiplication explicitly. You will get a result expressed in the [itex]a_{ij}[/itex] which will in fact be just a complete row or column from A. On the other hand, it should also be the new basis vector. So you can read off whether you need to put it in a column, or in a row.
  5. Mar 1, 2008 #4
    can you give an actual example to this
    and in simpler words

    because i cant understand how this multiplication effects the desition to put the vectors by rows or by columns

    using your multiplication i would get the first row of this matrix
    now what??
  6. Mar 1, 2008 #5


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    Staff Emeritus
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    He said: "Try both and see which gives what you want!"
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