People must get taught math terribly if they think "I don't need to worry about piles of abstract math to understand a rotation, all I have to do is think about what happens to the XYZ axes under the matrix rotation". That is what you should learn in the math class!

Anyone who has taken linear algebra should know that (1) a rotation is a linear operation, (2) the result of a linear operation is calculated with matrix multiplication, (3) the result of a matrix multiplication is determined by what it does to the standard basis vectors, the results of which form the columns of the matrix.

This guy makes it sound like he had to come up with these concepts from scratch, and it's some sort of pure visual genius rather than math. But... it's just math.

> Mathematicians like to see their matrices laid out on paper this way (with the array indices increasing down the columns instead of across the rows as a programmer would usually write them).

Could a mathematician please confirm of disconfirm this?

I think that different branches of mathematics have different rules about this, which is why careful writers make it explicit.

I don't think there's any mathematical reason to lay out the elements in memory that way. Sure given no context I would probably use i = row + n col as index, but it doesn't really matter much me.

If I had to pick between a matrix being a row of vectors or a column of covectors, I'd pick the latter. And M[i][j] should be the element in row i column j, which is nonnegotiable.

Part of a fairly old OpenGL tutorial, about 2002.

The age doesn't affect this matrix part, but just FYI that any specific APIs discussed will probably be out of date compared to modern GPU programming.

yellow text on green background... my eyes!