# Linear Algebra - Transformations

1. Feb 10, 2005

### merlinMan

We are doing linear transformations in geometry. We have a projection in three dimensional space onto a line. Do we basically treat this as the same as a two dimensional projection?

Also, anyone know of a really good linear algebra textbook that you could basically teach yourself from?

I'm stuck with a gradstudent who quite frankly is more concerned with his Phd process than putting effort into his teaching.

Thanks alot!

2. Feb 11, 2005

### Erienion

So you have a line in 3d space, which is just a 3x1 matrix.

when you want to transform this line you act on it with a transformation matrix, just the same as you would for a 2d line.

I think that a really good linear algebra book is LInear Algebra - David C. Lay

3. Feb 11, 2005

### Galileo

Any projection onto a subspace W of some vector space V can be treated the same.
But for projection on a line, the transformation matrix can be written in a more simple form, using the inner product (or dot product in R^3).

Also, for projection on plane, you can project along any two basis vectors in the plane and add the corresponding projections to get the answer.
So it basically becomes two line projections.