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A Lie algebra over an algebraically closed field is called exceptional if it is constructed from one of the root systems E_6, E_7, E_8, F_4, and G_2 by the Chevalley ...

The kth exterior power of an element alpha in an exterior algebra LambdaV is given by the wedge product of alpha with itself k times. Note that if alpha has odd degree, then ...

A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

The notion of a Hilbert C^*-module is a generalization of the notion of a Hilbert space. The first use of such objects was made by Kaplansky (1953). The research on Hilbert ...

The n-hypercube graph, also called the n-cube graph and commonly denoted Q_n or 2^n, is the graph whose vertices are the 2^k symbols epsilon_1, ..., epsilon_n where ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

The Knuth-Bendix completion algorithm attempts to transform a finite set of identities into a finitely terminating, confluent term rewriting system whose reductions preserve ...

A grand unified theory of mathematics which includes the search for a generalization of Artin reciprocity (known as Langlands reciprocity) to non-Abelian Galois extensions of ...

In calculus, geometry, and plotting contexts, the term "linear function" means a function whose graph is a straight line, i.e., a polynomial function of degree 0 or 1. A ...