Matrix "split"

[Santeri Piippo]

On the topic of matrix calculations, I believe it should be possible to split any given transformation matrix into two composing matrices where one would represent the rotation and the other would represent the scale. Essentially a matrix version of a "vector = unit_vector * scalar" equation, like a "matrix = rotation_matrix * scale_matrix" where rotation_matrix would contain the rotation of the matrix with no scaling and scale_matrix would be otherwise an identity matrix but with the scaling of the main matrix. Is this kind of split possible? If so, how to do it?