"All limits, especially national ones, are contrary to the nature of mathematics… Mathematics knows no races… For mathematics the whole cultural world is a single country" – David Hilbert. "Face problems with a minimum of blind calculation, a maximum of seeing thought" – Hermann Minkowski

Matrices and geometrical transformations – video clip

This shows how to translate between linear geometrical transformations (reflection, rotation, scaling, shearing, whatever) and 2×2 matrices (tables of numbers). Please work through it bit by bit, pausing as you go, with a pen and paper to hand.

Forgive me one blunder. When I show the whiteboard marker and the calculator being rotated anticlockwise, it appears clockwise to you, viewing the video!