MathJax 的基本運用

Reference:
https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference

1、 絕對值和範數（Absolute values and norms）

The absolute value of some expression can be denoted as \lvert x\rvert or, more generally, as \left\lvert … \right\rvert. It renders as |x|$|x|$ .

The norm of a vector (or similar) can be denoted as \lVert v\rVert or, more generally, as \left\lVert … \right\rVert. It renders as ∥v∥$\Vert v\Vert$ . (You may also write \left|…\right| instead.)

In both cases, the rendering is better than what you’d get from |x| or ||v|| , which render with bars that don’t descend low enough and sub-optimal spacing. |x|$|x|$ or ||v||$||v||$ .

It was typeset as

|x|,||v||⟶|x|,∥v∥$$|x|,||v||⟶|x|,\Vert v\Vert$$

2、Arbitrary Operator

If an operator is not available as a built-in command, use \operatorname{…}. So for things like

arsinh(x)$$\mathrm{a}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}(\mathrm{x})$$

write \operatorname{arsinh}(x) since \arsinh(x) will give an error and arsinh(x) has wrong font and spacing: arsinh(x).
For operators which need limits above and below the operator, use \operatorname*{…}, as in

Resz=1(1z2−z)=1$$\underset{z=1}{Res}\left(\frac{1}{z^2-z}\right)=1$$

爲什麼z=1$z=1$ 不是在Res$Res$ 的下面

max∥x∥=1∥Ax∥$$\underset{\Vert x\Vert =1}{max}\Vert Ax\Vert$$

max∥x∥=1∥Ax∥$$\underset{\Vert x\Vert =1}{max}\Vert Ax\Vert$$

∥x0∥$\Vert x_0\Vert$
ex=limn→∞(1+xn)n$e^x=\underset{n\to \mathrm{\infty }}{lim}{\left(1+\frac{x}{n}\right)}^n$

limx→1x2−1x−1$\underset{x\to 1}{lim}\frac{x^2-1}{x-1}$