Yup, I consider this interpretation as a matrix being a function that takes in objects like a line, a circle or a convex shape and spits out objects like some other line, an ellipse or another convex shape. It is a level of abstraction where you no longer care _how_ matrix multiplication works - you mostly care about what a matrix does to geometric objects. I covered this aspect not in the above article but in a separate one: https://www.linearalgebraforprogrammers.com/la/3_mat_vec_mul