OK, after refreshing my memory on GA, it seems that one of the nice things about it is that you don't have to think about the "row" vs "column" vectors present in "Vector Algebra". Which are usually represented in the form of matrices.
But you don't "need" them in GA, since you can directly work with vectors (= arrays) !
(Which makes it even more curious as to why matrices would be more efficient for 3D work ??)
I think I understand roughly what you mean when you distinguish row and column vectors. For example, let [x, y] represent a row vector and [x, y]^T represent a column vector.
If you have a function f that maps [x, y]^T -> z, (you might write it z=f(x,y)), then the gradient(f) is a function [x, y]^T -> [x, y]. That is to say, the gradient is a row vector. It's a different kind of vector than the input to f. And it transforms different (c.f. https://math.stackexchange.com/a/3200912/)
As you say, Geometric Algebra doesn't talk about row vectors and column vectors. For example, in 3D GA,you can choose a representation in R^8. That's 1 scalar, 1 pseudo-scalar, 3 column-y components, and 3 row-y components.
lol, ok - so then it's more the opposite - in GA there are row an column "vectors" (3-components)... but they are not "enough" (for that R^8 representation), so a matrix representation might be misleading ?
From reading a lot of comments it seems like misinformation. One thing worth keeping in mind is that game developers are highly risk averse. For good reason.
