eosbuddy is right. The one thing I would mention is that there is no GooCanvasTransformation Matrix. Goo is based on Cairo, and their is the Goo::Cairo::Matrix . Read the Cairo docs( although the explanation is minimal)

Goo and Cairo are still developing, so the matrices are still hidden behind the scenes, but in something more mature, like Tk::Zinc, you can save the state of the matrix any any point, and restore it later, and even create your own matrix manually.

Basically a matrix is some sin($angle), cos($angle), plus translation elements, that get applied to some vector. When at it's simplest( like a simple translation or rotation of a point about a center), it's easy..... but things become complicated very quickly, and it all ends up in giant matrix equations, that are not so simple for humans to understand, but computers find it easy. See matrix transformations . You can spend 8 years in college mastering it, then go to work for Steven Speilberg's Dreamworks, and do it on supercomputers, making state-of-the-art 3d animation.