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?

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HallsofIvy

Homework Helper
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".

Oerg

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

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

then a simple solution would be

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

because

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

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

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

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

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