by [Theo Verelst]

A common thing in math and science is the rotation of a vector over an angle, as most with a math basis knowledge will know, a matrix can be used for the purpose of performing the rotation on a vector.

A rotation matrix is even a very well formed matrix in general with normally excellent invertability eigenvalue computability.

It is not hard to make a orthogonal and even orthonomal basis for both the column and row space of a 2 dimensional matrix, and we can do so symbolically with simple geometic functions with a single rotation angle as a parameter for each of the 2x2 matrix elements.

Clear application is computer graphics, but other computations, for instance where complex numbers are used such as in electronics or other solutions of differential equations, also can become more insightfull by clear (simple) vector representations.

Bwise is about BlockWise programming, and also about Tk canvasses with interactions and graphical feedback, so this is a nice example.