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For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

In algebraic topology, the Reidemeister torsion is a notion originally introduced as a topological invariant of 3-manifolds which has now been widely adapted to a variety of ...

A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...

A transpose of a doubly indexed object is the object obtained by replacing all elements a_(ij) with a_(ji). For a second-tensor rank tensor a_(ij), the tensor transpose is ...

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

A general n-gonal antiprism is a polyhedron consisting of identical top and bottom n-gonal faces whose periphery is bounded by a band of 2n triangles with alternating up-down ...

A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

Chebyshev iteration is a method for solving nonsymmetric problems (Golub and van Loan 1996, §10.1.5; Varga, 1962, Ch. 5). Chebyshev iteration avoids the computation of inner ...