# multiplicativity

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**Degree of a field extension**— In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the size of the extension. The concept plays an important role in many parts of mathematics, including algebra and number theory indeed in any… … Wikipedia**Expected value**— This article is about the term used in probability theory and statistics. For other uses, see Expected value (disambiguation). In probability theory, the expected value (or expectation, or mathematical expectation, or mean, or the first moment)… … Wikipedia**Cauchy-Binet formula**— In linear algebra, the Cauchy Binet formula generalizes the multiplicativity of the determinant (the fact that the determinant of a product of two square matrices is equal to the product of the two determinants) to non square matrices. Suppose A… … Wikipedia**Determinant**— This article is about determinants in mathematics. For determinants in epidemiology, see Risk factor. In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific… … Wikipedia**Quaternion**— Quaternions, in mathematics, are a non commutative extension of complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three dimensional space. They find uses in both… … Wikipedia**Cross product**— This article is about the cross product of two vectors in three dimensional Euclidean space. For other uses, see Cross product (disambiguation). In mathematics, the cross product, vector product, or Gibbs vector product is a binary operation on… … Wikipedia**Dirichlet convolution**— In mathematics, the Dirichlet convolution is a binary operation defined for arithmetic functions; it is important in number theory. It was developed by Johann Peter Gustav Lejeune Dirichlet, a German mathematician. Contents 1 Definition 2… … Wikipedia**Algebraic torus**— In mathematics, an algebraic torus is a type of commutative affine algebraic group. These groups were named by analogy with the theory of tori in Lie group theory (see maximal torus). The theory of tori is in some sense opposite to that of… … Wikipedia**Hecke operator**— In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by Hecke (1937), is a certain kind of averaging operator that plays a significant role in the structure of vector spaces of modular forms and more… … Wikipedia**Lagrange's identity**— In algebra, Lagrange s identity is the identity:iggl( sum {k=1}^n a k^2iggr) iggl(sum {k=1}^n b k^2iggr) iggl(sum {k=1}^n a k b kiggr)^2 = sum {i=1}^{n 1} sum {j=i+1}^n (a i b j a j b i)^2 iggl(= {1 over 2} sum {i=1}^n sum {j=1}^n (a i b j … Wikipedia