[bob1029]

I think a good project-based way to learn about linear algebra is to build a 3d scene rasterizer from scratch. Once you get nested transforms and projection matrices figured out, you are probably going to have a much deeper sense for what these things actually are than someone walking out of a typical college course. The 4x4 homogenous transformation matrix sort of tricked me into learning about things I didn't originally intend to. I spent a solid week watching videos (such as the exact one you linked above) to reach a more satisfying understanding.

I vividly recall manipulating matrices on paper for weeks in college. Absolutely none of it had any real meaning to me. Very little of that education helped me as I got into actual projects, other than some vague awareness that there are these things called matrices and something about system of equations. Having something to pull me towards a specific objective has always resulted in a much more substantial education. Learning about some of this stuff in isolation is really quite painful. Learning about painful things to get to the fun bits seems more tenable.

[jesuslop]

The homogeneous thing is very nice. As you know it let's you pack translations and self linear maps in K^n into the linear maps of K^(n+1). OpenGL uses it. Also if your perspective is isometric (the projection of the 3D canonic base reminds a Mercedes-Benz logo) it is just linear K^3->K^2.

[zvmaz]

> I think a good project-based way to learn about linear algebra is to build a 3d scene rasterizer from scratch. Once you get nested transforms and projection matrices figured out, you are probably going to have a much deeper sense for what these things actually are than someone walking out of a typical college cours

I don't think this is the best way to learn about linear algebra. It's still mystifying.