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

[Oerg]

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]

"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".

 

[Oerg]

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

$$x=t$$
$$y=t$$
$$z=t$$

then a simple solution would be

$$[T]=\left[ \begin{array}{ccc}<br /> 1 & 1 & 1 \\<br /> 1 & 1 & 1 \\<br /> 1 & 1 & 1<br /> \end{array} \right]$$

because

$$T(e_1)=\left[\begin{array}{ccc}<br /> 1\\1\\1 \end{array}\right]$$

$$T(e_2)=\left[\begin{array}{ccc}<br /> 1\\1\\1 \end{array}\right]$$

$$T(e_3)=\left[\begin{array}{ccc}<br /> 1\\1\\1 \end{array}\right]$$

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