LaTeX cheat sheet « Latex « katanshin.co.uk

LaTeX cheat sheet

I don’t mind admitting that I don’t have any formal academic qualifications in maths, barring A-Level. And let’s face it back then I was more interested in girls than differential equations so I didn’t do brilliantly.

However, lately I find myself needing a lot of linear algebra and playing with matrices – so. Time to make things easy for myself and make a cheat-sheet of all the stuff I’ll need.

Maybe it’ll be of some small use to someone else, but usual disclaimers as to accuracy apply. Up to a few weeks ago the math notation used in most text books was all Greek to me (oho!), so forgive me if this is elementary.

A great resource for this stuff is here, and another good one is here. Also, when you’re trying to find out the $\LaTeX$ command for a particular symbol, try detexify - you can draw what you want and it’ll present you with a list of trained examples! Very nice, comes in iPad flavour too. I’ve tried out a few of the examples on this page, as an exercise.

I’m using quick LaTeX which is by far the best plugin I’ve tried. Thoroughly recommended.

My favourite $\LaTeX$ symbol is $\Im$ . Good to know.

Symbols

$\alpha, \Alpha, \beta, \Beta, \gamma, \Gamma, \pi, \Pi, \phi, \varphi, \Phi$ means:

alpha, Alpha, beta, Beta, gamma, Gamma, pi, Pi, phi, varphi, Phi. (Missing characters mean just use normal uppercase roman characters, like $A$

Lambda ( $\lambda$ )-ish calc notation

$\forall x \in X,\quad \exists y \leq \epsilon$ means:

For all x in X, exists Y less than equal to epsilon

$A \subset B$ and $A \subseteq B$ denote A is a subset of B. However, $\subset$ is more properly used to denote a proper subset. (Set Theory)

Geometry

Thus, something like $\{x_i\}_{i=1}^{m} \subseteq \mathds{R}$ should refer to a vector of values for x indexed at 1 and of m length, that is a subset of real numbers. However, $\mathds{R}^n$ would refer instead to the Cartesian product of n copies of R, i.e. essentially an n-length cartesian coordinate describing a point in n-dimensional space. That is to say, when used in the context of the above example, we are now looking at a vector of coordinates in n-dimensional space, where i is a number between 1 and m, and $x_i$ is a cartesian coordinate describing a point in space.

Math

$\sum_{i=1}^{10} t_i$ means:

The sum of all values for $t$ where the value of $i$ is between 1 and 10.

$\prod_{i=1}^{n} t_i$ means:

The same except the range of values is the variable $n$ and you multiply each value instead of summing it.

$\sqrt{ \dfrac{\sum_{i=1}^{j}(n_i)\vspace{20pt}}{\vspace{20pt}\prod_{i=1}^{j}( n_i)}}$ means:

The root of n divided by the product of all values of n.

$x \equiv y$ means:

The equivalent of

$E(...)$ refers to:

Expected values of whatever

$\|x\|$ means:

The magnitude/length of x, or more correctly its norm (length seems more meaningful, but who am I to argue?)

$\mid x\mid$ means:

Can mean the same as the above! Or an absolute value of a scalar; or the determinant of a matrix.

$\|x_i-y_i\|$ means:

The distance between x and y (or the magnitude of the delta of x and y, same thing)

$x \ldotp y$ means:

The dot product of x and y.

$\bar x$

Can mean the compliment of x (i.e. a subset of it); hence the symbol for mean, which refers to a subset of the total population of x?

Matrices

Capitalised characters $M, I$ are used to denote a Matrix. Lowercase roman letters denote variables or vectors, such as in: $x, k$

Generic matrix with equation numbering:

(1) $\begin{equation*} A_{m,n} = \begin{pmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{pmatrix} \end{equation*}$

Variation… m, n, refer to rows, cols

(2) $\begin{equation*} B_{2,4} = \begin{bmatrix} 1, 2, 3, 4\\ 5, 6, 7, 8 \end{bmatrix} \end{equation*}$

Probability

$P(y=1|x;\theta) = 0.7$ means the probability that y is equal to 1, given x parameterised by theta, is 0.7
$x \sim \mathscr{N}(\mu,\sigma^{2})$ x is distributed as N(params).
Geometry

Aymptote = curve that approaches zero distance to a line or axis as it approaches infinity.

This entry was posted on Monday, October 24th, 2011 at 11:06 am and is filed under LaTeX, Math. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

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