User:Howard Geraint Ricketts~enwiki/Test page

stuff
The basics and examples of writing Mathematical stuff is found at Help:Formula.

"Matrixy" stuff

 * $$I_2 \equiv \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$$

eigenvalues and eigenvectors
for example let M be some kind of 2 x 2 matrix
 * $$M \equiv \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix}$$

now let us suppose that p is a two dimensional vector there may be certain values of p such that
 * $$M p = \lambda p\,$$

in two dimensions this is like saying that there are certain lines that are invariant under the transformation M. Of course the individual points may move under a transformation (unless $$\lambda = 1$$) but the actual line will remain unaltered.