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In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
If () = ([,]) (that is, the infimum of f over [,]), the method is the lower rule and gives a lower Riemann sum or lower Darboux sum. All these Riemann summation methods are among the most basic ways to accomplish numerical integration .
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
The direct sum is also commutative up to isomorphism, i.e. for any algebraic structures and of the same kind. The direct sum of finitely many abelian groups, vector spaces, or modules is canonically isomorphic to the corresponding direct product. This is false, however, for some algebraic objects, like nonabelian groups.
The sum a + b can be interpreted as a binary operation that combines a and b, in an algebraic sense, or it can be interpreted as the addition of b more units to a. Under the latter interpretation, the parts of a sum a + b play asymmetric roles, and the operation a + b is viewed as applying the unary operation +b to a. [20]
Empty sum, a sum with no terms; Indefinite sum, the inverse of a finite difference; Kronecker sum, an operation considered a kind of addition for matrices; Matrix addition, in linear algebra; Minkowski addition, a sum of two subsets of a vector space; Power sum symmetric polynomial, in commutative algebra; Prefix sum, in computing
In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
represents: the Kappa number, indicating lignin content in pulp; represents: the Von Kármán constant, describing the velocity profile of turbulent flow; the kappa curve, a two-dimensional algebraic curve; the condition number of a matrix in numerical analysis; the connectivity of a graph in graph theory