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Free product. In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains both G and H as subgroups, is generated by the elements of these subgroups, and is the “ universal ” group having these properties, in the sense that any two ...
Differential forms can be multiplied together using the exterior product, and for any differential k-form α, there is a differential (k + 1)-form dα called the exterior derivative of α. Differential forms, the exterior product and the exterior derivative are independent of a choice of coordinates.
Normal order. In quantum field theory a product of quantum fields, or equivalently their creation and annihilation operators, is usually said to be normal ordered (also called Wick order) when all creation operators are to the left of all annihilation operators in the product. The process of putting a product into normal order is called normal ...
t. e. In mathematics, specifically in group theory, the direct product is an operation that takes two groups G and H and constructs a new group, usually denoted G × H. This operation is the group-theoretic analogue of the Cartesian product of sets and is one of several important notions of direct product in mathematics.
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In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial ). For example, is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K, such as the real or complex numbers, and one speaks of a quadratic form over K.
Formal definition. The exterior algebra of a vector space over a field is defined as the quotient algebra of the tensor algebra by the two-sided ideal generated by all elements of the form such that . [ 6] Symbolically, The exterior product of two elements of is defined by.
Canonical normal form. In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form ( CDNF ), [ 1] minterm canonical form, or Sum of Products ( SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form, or Product of Sums ...