[Question] Matrix4f.determinate() looks wrong? about joml HOT 2 CLOSED

You are right in that both Matrix4f.determinant() and Matrix4f.invert() would need to effectively do the same computations. And they indeed do. It's just that the calculations done in Matrix4f.invert() have been massively reshuffled and reorganized to make full use of variables to hold common sub-expressions that are computed at least twice. This gave a huge performance boost compared to a naive implementation of Matrix4f.invert() where you'd simply once call determinant() and then do all computations for the individual matrix elements.
However, both the determinant and the inverse matrix elements share many common sub-expressions that need not be computed multiple times, so I spend literally hours refactoring it to have as few arithmetic operations and as many reuses of variables for common sub-expressions as possible.

The fact that you do not see the common alternating + - patterns in the determinant is that this has also been restructured/reshuffled to "look nicer". Note that + (a * b - c * d) is equal to - (c * d - a * b). This is all there is to it, really.

And both methods should do what they are supposed to do.

from joml.

Note that + (a * b - c * d) is equal to - (c * d - a * b). This is all there is to it, really.

This makes so much more sense now and I didn't even think about that. Nor did I think about the performance implications. Thank you for clarifying!

from joml.