User:Sintel/Conventions

I'm gonna put this here since I keep forgetting where I commented this originally.

Math conventions

There are currently no real conventions for mathematical notation. Since a lot of math pages involve linear algebra, I propose the following:

Open up any introductory linear algebra textbook. Follow the notation that is used there.

In practice this means:

• Matrices are uppercase Roman letters: [math]\displaystyle{ M }[/math].
• Vectors (whether column or row) are usually lowercase Roman letters: [math]\displaystyle{ u }[/math].
• When there is potential confusion with scalars, they can be made boldface: [math]\displaystyle{ \mathbf{u} }[/math], or get an arrow: [math]\displaystyle{ \overrightarrow{u} }[/math].
• Inner product can be notated: [math]\displaystyle{ u^\mathsf{T}v }[/math] or [math]\displaystyle{ \left\langle u,v \right\rangle }[/math].
• The p-norm is: [math]\displaystyle{ \| u \|_p }[/math], when no p is given, 2-norm is assumed.
• When writing a column vector inside text, just transpose it: [math]\displaystyle{ w =\begin{bmatrix} w_1 & w_2 & w_3 \end{bmatrix}^{\mathsf{T}} }[/math].

The wiki has Mathjax support, use it!

This also means getting rid of bra-ket notation, by the way. They are used to denote quantum states in complex Hilbert spaces. We are not doing quantum physics here so let's stop pretending.