A transformation matrix transforms a vector of point coordinates in given frame of reference into coordinates in another one (e.g. from child to parent in our beloved display lists or scene graphs) – Captain Obvious.
Many people think of transformation matrices as impenetrable black boxes filled with random numbers that are impossible to make sense of while fiddling with your application. So this 1st post of the year is my attempt to help those people, by providing as short and simple explanation for those numbers as possible.
P.S. Since matrices transform vectors, you need to know a thing or two about vectors 1st.