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Given a function f(x_1,...,x_n) defined on a domain U, the graph of f is defined as the set of points (which often form a curve or surface) showing the values taken by f over ...

Gaussian elimination is a method for solving matrix equations of the form Ax=b. (1) To perform Gaussian elimination starting with the system of equations [a_(11) a_(12) ... ...

A path in a graph G is a subgraph of G that is a path graph (West 2000, p. 20). The length of a path is the number of edges it contains. In most contexts, a path must contain ...

The set of graph eigenvalues of the adjacency matrix is called the spectrum of the graph. (But note that in physics, the eigenvalues of the Laplacian matrix of a graph are ...

The Grassmannian Gr(n,k) is the set of k-dimensional subspaces in an n-dimensional vector space. For example, the set of lines Gr(n+1,1) is projective space. The real ...

There are essentially three types of Fisher-Tippett extreme value distributions. The most common is the type I distribution, which are sometimes referred to as Gumbel types ...

The Heawood four-color graph is the 25-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's ...

Let |A| denote the cardinal number of set A, then it follows immediately that |A union B|=|A|+|B|-|A intersection B|, (1) where union denotes union, and intersection denotes ...

The proof theories of propositional calculus and first-order logic are often referred to as classical logic. Intuitionistic propositional logic can be described as classical ...

A branch of mathematics which brings together ideas from algebraic geometry, linear algebra, and number theory. In general, there are two main types of K-theory: topological ...