Mathematics. Dictionary

Given a random sample \textstyle \mathbf{x}_{1},\ldots,\mathbf{x}_{N} from an \textstyle n-dimensional random variable \textstyle \mathbf{X}, a mean defined as

A function that assigns a scalar value to every point in space.

Multiplication of a vector by a scalar (which belongs to the vector space's field of scalars).

The dot product of one of the three vectors with the cross product of the other two.

A type of display using Cartesian coordinates to display values for two variables for a set of data.

An ordered list of objects, typically indexed with natural numbers.

The mathematical theory of sets.

A set of general techniques for computing or estimating the size of sifted sets of integers.

A measure of how likely it is to draw a false conclusion in a statistical test, when the results are really just random variations.

A generalization of a triangle or tetrahedron to an arbitrary dimension; more accurately, the convex hull of n+1 affinely independent points in n-dimensional space.

A particular type of factorisation of a matrix into a product of three matrices, of which the second is a diagonal matrix that has as the entries on its diagonal the singular values of the original matrix.

A square matrix equal to the negative of its transpose.

A function that has derivatives of all finite orders everywhere in its domain.

A group G which is part of a finite chain Gi (0 ≤ i ≤ n) of subgroups, where G0 is the trivial subgroup and Gn = G, such that each intermediate subgroup Gi is a normal subgroup of the next in the chain (i.e., Gi ◁ Gi+1) and each quotient Gi+1/Gi is a cyclic group.

Any curve in three-dimensional space; includes any plane curve as a subset.

A theorem providing conditions under which an operator or matrix can be diagonalized.

The arranging of non-overlapping spheres in space

A measure of how spread out data values are around the mean, defined as the square root of the variance. Represented with the Greek letter σ.

The normal distribution with a mean of zero and a variance of one.

A point on a curve where the gradient is zero. This point can be a maximum, a minimum, or a point of inflection.

A function that maps elements of an index set to elements of a collection of random variables; historically, a collection of random variables indexed by a set of numbers usually regarded as points in time.

A matrix formed by selecting certain rows and columns from a larger matrix.

The topology of a subset S of a topological space X which is obtained by considering any subset of S to be an open set if it corresponds to the intersection of S with some open set of X.

An integral over a 2-dimensional domain

A formal system of deductive logic in which aspects and relationships of natural language are represented by a system of symbols.

The set that contains all elements belonging to either of given two sets but not to the both; the relative complement of the intersection in the union of given two sets.

A group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections.

A square matrix that is its own transpose, and is thereby symmetric about the main diagonal

A group whose elements are all the transformations under which a given object remains invariant and whose group operation is function composition.