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Multiplication operator (471 bytes)
1: ...Multiplication operators generalize the notion of operator given by a [[diagonal matrix]]. 3: See also: [[translation operator]], [[shift operator]]. Multiplication (8176 bytes) 2: In its simplest form, '''multiplication''' is a quick way of [[addition|adding]] identica... 6: Multiplication can be denoted in several equivalent ways. All of... 13: ...he [[FORTRAN]] programming language.) Frequently, multiplication is implied rather than shown in a notation. This ... 47: As for what multiplication means, the product of two whole numbers n and m i... 63: ...t is easy to prove some interesting properties of multiplication. As the first two examples above hint at, the ord... Peasant multiplication (2198 bytes) 3: ...for [[multiplication]]. It requires no use of a [[multiplication table]]; however, it requires that the user be ab... 21: The method works because multiplication is [[distributivity|distributive]], so: 37: See also: [[Multiplication algorithm]], [[Binary numeral system]]. Multiplication algorithm (7763 bytes) 1: ...algorithm''' is an [[algorithm]] (or method) to [[multiplication|multiply]] two numbers. Depending on the size of ... 3: ...of multiplying two ''n''-digit numbers using long multiplication is [[Big O notation|Θ]](''n''<sup>2</sup>). 5: ...ication]] algorithm; this is actually a method of multiplication using base 2. 8: These systems employ '''Karatsuba multiplication''' which was discovered in 1962 and proceeds as f... 13: ...this can be done with only three rather than four multiplications: Multiplication table (6643 bytes) 1: ... a '''multiplication table''' is used to define a multiplication [[binary operation|operation]] for an algebraic s... 5: ...lication table (as used to teach schoolchildren [[multiplication]]) is a grid where rows and columns are headed by... 172: A table of multiplication is one of the number from 1 through 10 multiplied... 176: The traditional [[rote learning]] of multiplication was based on memorisation of columns in the table... 193: For example, for multiplication by 6 a pattern emerges: Complex multiplication (2778 bytes) 1: ...aid to have remarked that ''the theory of complex multiplication is the most beautiful part of mathematics''. 3: An example of an elliptic curve with complex multiplication is 15: ...]s. This is a typical elliptic curve with complex multiplication, in the sense that over the complex number field ... 17: ...own that, in a general sense, the case of complex multiplication is the hardest to resolve for the [[Hodge conject... Matrix multiplication (7683 bytes) 5: ...tant way to multiply matrices is the usual matrix multiplication. It is defined between two matrices only if the n... 9: ...ummarises the abstract properties of this kind of multiplication. 13: :[[Image:Matrix multiplication diagram.PNG]] 38: ...ith ''B'' being applied first. In general, matrix multiplication is not [[commutative]]; that is, AB is not equal ... 40: ...in [[1969]] and often referred to as "fast matrix multiplication", uses a mapping of bilinear combinations to redu... Multiplication ALU (3392 bytes) 1: ...ircuit|digital design]], a '''multiplier''' or '''multiplication ALU''' is a hardware circuit dedicated to multipl... 3: ...ght to primary schoolchildren for conducting long multiplication on base-10 integers, but has been modified here f... 6: ...ight partial products by performing eight one-bit multiplications, one for each bit in multiplicand ''a'': Scalar multiplication (2410 bytes) 1: ...e]] in [[abstract algebra]]). Note that '''scalar multiplication''' is different than '''[[scalar product]]''' whi... 3: ...</i> is a vector space over <i>K</i>, then scalar multiplication is a [[function (mathematics)|function]] from <i>... 6: Scalar multiplication obeys the following rules ''(vector in [[boldface... 14: ...n indicates either scalar multiplication or the [[multiplication]] operation in the field. 16: ...pace. A [[geometric]] interpertation to '''scalar multiplication''' is a streching or shrinking of a vector. E-Plus (operator) (433 bytes) 1: ...as of [[2004]] E-Plus is the third largest mobile operator in Germany, after [[T-Mobile]] (26.7 million subs... 3: ...owned by [[Netherlands|Dutch]] telecommunications operator [[KPN]]. Mu operator (684 bytes) 1: ...bility theory]], the '''μ-operator''' is the [[operator]] which when applied to a given [[computable func... Operator (11813 bytes) 1: ...mathematics]], for other kinds of operators see [[operator (disambiguation)]].'' 3: ...a mapping between [[vector space]]s; this kind of operator is distinguished by taking one vector and returni... 5: ... Functions can therefore conversely be considered operators, for which we forget some of the type baggage, l... 7: ==Operators and levels of abstraction== 9: ...ge of ''[[function (mathematics)|function]]'': an operator can be taken to be some special kind of function.... Operator No. 5 (392 bytes) 1: '''Operator No. 5''' was a pulp magazine that was published b... Closure operator (4422 bytes) 1: ...rtially ordered set]] (''P'', ≤), a '''closure operator''' on ''P'' is a [[function (mathematics)|functio... 8: ...lusion ⊆. (Note that the topological closure operator is ''not'' characterized by these properties howe... 10: ...an be derived from ''X''. Then ''C'' is a closure operator on ''P''. 12: ...f ''G'' containing ''X''. Then ''C'' is a closure operator on the set of subsets of ''G'', ordered by inclus... 14: ... [[integer]] not smaller than ''x'', is a closure operator as well. Switchboard operator (509 bytes) 1: ...o-large organisations often employ '''switchboard operators'''—specialised staff who answer general [[... Operator (disambiguation) (1045 bytes) 1: An '''operator''' refers to more than one thing: 3: ...ter programming]], an '''[[operator (programming)|operator]]''' is a type of [[function (programming)|functi... 4: *In [[mathematics]], an '''[[operator]]''' is some kind of [[function (mathematics)|fun... 5: *In [[genetics]] an '''[[operator (genetics)|operator]]''' is the site on [[DNA]] to which a specific [... 6: *In [[physics]], an '''[[operator (physics)|operator]]''' often takes on a more specialized meaning th... Compact operator (2453 bytes) 1: [[Category:Operator theory]] 3: ...osure in the [[operator norm]] of the finite rank operators. Whether this was true in general for Banach spa... 5: ...f such equations. The abstract idea of [[Fredholm operator]] is derived from this connection. 7: ...as a finite-dimensional [[kernel (algebra)#Linear operators|kernel]] for all complex λ ≠ 0). 9: ...rs between two Banach spaces. Indeed, the compact operators on a Hilbert space form a [[maximal ideal]], so ... Operator algebra (2141 bytes) 1: ..., even more specially in reference to algebras of operators on a Hilbert space. 3: ...pectral theory]] of a single operator. In general operator algebras are non-commutative rings. 5: ...nn algebra, but this is somewhat more technical. Operator algebras on a Hilbert space which are invariant u... 7: Examples of operator algebras which are not self-adjoint include: 14: *[[Topologies on the set of operators on a Hilbert space]] Shift operator (3192 bytes) 1: [[Category:Unitary operators]] 2: [[Category:Isometric operators]] 3: ...er usage of ''shift operator'' as a [[translation operator]]: see for example [[Sheffer sequence]].) 5: A typical '''one-sided shift''' operator takes an [[infinite sequence]] of numbers 13: ...series]]; it therefore gives rise to [[continuous operator]]s on the standard sequence spaces used in functi... IRC Operator (973 bytes) 1: '''IRC Operators''' are users on an [[Internet Relay Chat]] (IRC)... 3: Operators access and powers differ based on the server sof... 5: ...sers on the server their access is on, and Global operators who can affect any user on the network. 7: For the most part Operators have the ability to issue a kill command that fo... 9: A list of operators on a particular server can traditionally be view...
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