User:Howard Geraint Ricketts/Test page

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[edit] stuff

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


[edit] "Matrixy" stuff

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

[edit] 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 λ = 1) but the actual line will remain unaltered.

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