# Matrix multiplication order for multiple model transformations

I have a problem in terms of what frame of reference, I should construct, scaling (S), rotation (R) and translation (T) for a model matrix (in that order). Let us assume the use of glm (or glsl), i.e. to mean column major representation.

I believe, it should be a matrix multiplication of:

M = T * R * S // S * R * T is what we want to apply, but due to being column major, the order gets reversed, due to (AB)^T =B^T*A^T


Now, if I have a previous transformation already applied (say M_prev), and I want to apply a transformation M on top of that, then is the correct form:

M_new = M_prev * M // M_new and M_prev are both column major. I'm post multiplying due to being column major, but this is incorrect, I guess?


I believe this is incorrect (at least in some experiments I carried out, please correct me if I'm wrong), and it should be the reverse. What is the flaw in my calculation of M_new?

• Your two examples aren't consistent with one another. If T*R*S means T is being applied after R which is in turn applied after S, then M_prev * M means M_prev is being applied after M; or vice versa, assuming all of your matrices are constructed similarly. Are you expecting that somewhere in between the matrices are being transposed? You mention one set being column-major and another row-major, but it's not clear why your application would be mixing two different matrix conventions. – DMGregory Sep 20 '17 at 0:38
• All matrices that I'm using are column major. Nothing is row major. I'm trying to understand why the 2nd equation is wrong. I added a comment to further clarify. I'm trying to applying S, then R and then T. But, reversing that order due to column major. – dev_nut Sep 20 '17 at 0:42
• I further added more. Nothing is row major. Everything is column major. Maybe, I'm doing the 2nd part correct for a 'row major' matrix, but that's what I'm trying to understand. Why is this wrong for column major? – dev_nut Sep 20 '17 at 0:45
• If the column major order for TRS is "later * earlier" then why would you expect that for M_prev and M it would become "earlier * later"? ie. T is supposed to happen after R, so you put it on the left. M is supposed to happen after M_prev, so why do you put it on the right? If you're using the same matrix convention throughout then your order of multiplication should not change. Where has our reasoning diverged? – DMGregory Sep 20 '17 at 0:48
• I'll confess I still don't understand what the question or confusion was in the first place, so I'm not sure what needs to be explained in an answer. – DMGregory Sep 20 '17 at 17:40

M_new = M_prev * M would apply first matrix M then M_prev which is not want what you want - think of them as some transformation matrices, like S, T, R and nothing more ...
Therefore if you want M be applied after 'M_prev' just do
M_new = M * M_prev