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Map vector A onto line l would that mean the projection of A

  1. Mar 13, 2009 #1
    If i were to say: Map vector A onto line l

    would that mean the projection of A onto l or the rotation of A onto l?
     
  2. jcsd
  3. Mar 13, 2009 #2

    HallsofIvy

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    Staff Emeritus
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    Re: Terminology

    "Map vector v onto line l" doesn't necessarily mean either of those- it just means that some function changes vector v to part of line l.

    I would say either "project vector v onto line l" or "rotate vector v onto line l".
     
  4. Mar 13, 2009 #3
    Re: Terminology

    Then what if we want a standard matrix for the linear transformation for any vector onto the line? let's say we have

    [tex]x=t[/tex]
    [tex]y=t[/tex]
    [tex]z=t[/tex]

    then a simple solution would be

    [tex][T]=\left[ \begin{array}{ccc}
    1 & 1 & 1 \\
    1 & 1 & 1 \\
    1 & 1 & 1
    \end{array} \right][/tex]

    because

    [tex]T(e_1)=\left[\begin{array}{ccc}
    1\\1\\1 \end{array}\right][/tex]

    [tex]T(e_2)=\left[\begin{array}{ccc}
    1\\1\\1 \end{array}\right][/tex]

    [tex]T(e_3)=\left[\begin{array}{ccc}
    1\\1\\1 \end{array}\right][/tex]

    this seems like a pretty simple solution, it maps the vector onto the line, but it is not a projection or a rotation.
     
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