I need some help understanding matrices in depth. I understand fully how matrices work (how they are added, multiplied, etc). But what I don't quite understand is the underlying relationship in translation matrices. The kind of stuff that the great mathematicians would have spent days trying to figure out. For example:
is the matrix that would rotate a 2-dimensional object clockwise with a magnitude of θ. But what is the relationship here that cause the object to be rotated? I know you simply multiply it by the x and y coordinates. But the main question is, what is the underlying relationship that cause this to work?[cosθ sinθ]
[-sinθ cosθ]