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

  • Thread starter Oerg
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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?
 

HallsofIvy

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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".
 
345
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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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