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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.
In mathematics, the term linear function refers to two distinct but related notions: [1] In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. [2] For distinguishing such a linear function from the other concept, the term affine function is often used ...
In mathematics, a group G is called the direct sum [1] [2] of two normal subgroups with trivial intersection if it is generated by the subgroups. In abstract algebra, this method of construction of groups can be generalized to direct sums of vector spaces, modules, and other structures; see the article direct sum of modules for more information.
The direct sum is an operation between structures in abstract algebra, a branch of mathematics. It is defined differently, but analogously, for different kinds of structures. It is defined differently, but analogously, for different kinds of structures.
In linear algebra, an element of a vector space, a sum of finitely many elements from a given basis set multiplied by real, complex, or other numerical coefficients. In the study of series (mathematics) , a sum of an infinite sequence of numbers or other quantities, considered as an abstract mathematical object regardless of whether the sum ...
In the long run, exponential growth of any kind will overtake linear growth of any kind (that is the basis of the Malthusian catastrophe) as well as any polynomial growth, that is, for all α: = There is a whole hierarchy of conceivable growth rates that are slower than exponential and faster than linear (in the long run).
2. In geometry and linear algebra, denotes the cross product. 3. In set theory and category theory, denotes the Cartesian product and the direct product. See also × in § Set theory. · 1. Denotes multiplication and is read as times; for example, 3 ⋅ 2. 2. In geometry and linear algebra, denotes the dot product. 3.
In mathematics, the term linear is used in two distinct senses for two different properties: . linearity of a function (or mapping);; linearity of a polynomial.; An example of a linear function is the function defined by () = (,) that maps the real line to a line in the Euclidean plane R 2 that passes through the origin.
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