Goo::Canvas Graphing demo tells me that Goo::Canvas is a graphing tool for conversion of graphs (typically this involves translation or rotation of images). Translation or rotation of images in mathematical terms implies taking an old array and moving it into a new array (the new array will contain the rotated or translated image). The old array -> new array is achieved by matrix multiplication:

new_array = transformation_matrix * old_array
[download]

So the transformation matrix is just a multiplicant to create the new array - hope that makes sense. Numerically, this matrix will depend on what you're trying to achieve (so I could explain it to you only conceptually).