I have a $2\times 3$ affine matrix $$ M = \pmatrix{a &b &c\\ d &e &f} $$ which transforms a point $(x,y)$ into $x' = a x + by + c, y' = d x + e y + f$
Is there a way to decompose such matrix into shear, rotation, translation,and scale ? I know there's something for $4\times 4$ matrixes, but for a $2\times 3$ matrix ?