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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.  There’s a very good cookbook whose format I should probably emulate here.  Also, when you’re trying to find out the 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  symbol is . Good to know.

Symbols

means:

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

Lambda ()-ish calc notation

means:

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

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

Geometry

Thus, something like should refer to a vector of values for x indexed at 1 and of m length, that is a subset of real numbers.  However, 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 is a cartesian coordinate describing a point in space.

Math

means:

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

means:

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

means:

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

means:

The equivalent of

refers to:

Expected values of whatever

means:

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

means:

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

means:

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

means:

The dot product of x and y.

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 are used to denote a Matrix.  Lowercase roman letters denote variables or vectors, such as in:

Generic matrix with equation numbering:

(1)  

Variation… m, n, refer to rows, cols

(2)  

Probability

means the probability that y is equal to 1, given x parameterised by theta, is 0.7
x is distributed as N(params).
Geometry

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