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The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...

A differential k-form omega of degree p in an exterior algebra ^ V is decomposable if there exist p one-forms alpha_i such that omega=alpha_1 ^ ... ^ alpha_p, (1) where alpha ...

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 ...

The wedge product is the product in an exterior algebra. If alpha and beta are differential k-forms of degrees p and q, respectively, then alpha ^ beta=(-1)^(pq)beta ^ alpha. ...

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 ...

In logic, a term is a variable, constant, or the result of acting on variables and constants by function symbols. In algebra, a term is a product of the form x^n (in the ...

The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A^(-1) such that AA^(-1)=I, (1) where I is the identity matrix. Courant and Hilbert (1989, ...

In the study of non-associative algebra, there are at least two different notions of what the half-Bol identity is. Throughout, let L be an algebraic loop and let x, y, and z ...

Suppose that A and B are two normed (Banach) algebras. A vector space X is called an A-B-bimodule whenever it is simultaneously a normed (Banach) left A-module, a normed ...