 |
|
| |
|
||||
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... 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... Multiplication operator (471 bytes) 1: ...often contrasted with [[composition operators]]. Multiplication operators generalize the notion of operator given... 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'': 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: 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: 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]]. 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... 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. Jordan algebra (1480 bytes) 1: ...act algebra]] as an [[algebra over a field]] with multiplication satisfying the following axioms: 8: ...ath> with the same underlying addition, and a new multiplication <math>(x . y)</math> as follows. 20: ...nt]] real, complex, or quaternionic matrices with multiplication 26: ...djoint matrices over the [[octonions]] again with multiplication Product (mathematics) (1563 bytes) 1: ...s; in other words, matrix multiplication, and the multiplications in those other algebras, are non-commutative. 5: ...[dot product]] and [[cross product]] are forms of multiplication of [[vector (spatial)|vector]]s. 6: ...f [[matrix (mathematics)|matrices]]; see [[matrix multiplication]]. Dozenal Society of Great Britain (512 bytes) 3: ...or example, in dozenal maths, 1/3 is 0.4, and the multiplication table shows more regularities and is therefore ea... Convolution theorem (1464 bytes) 1: ...e domain (i.e. [[time domain]]) equals point-wise multiplication in the other domain (i.e. [[frequency domain]]). 4: ...sk]] denotes convolution in this context, and not multiplication.) 8: where · denotes point-wise multiplication. It also works "the other way round": 16: ...''n''). This can be exploited to construct fast [[multiplication algorithm]]s. Nonassociative ring (2154 bytes) 3: ... is a set ''R'' with two operations, addition and multiplication, such that: 10: # Multiplication is linear in each variable: 14: Unlike for rings, we do not require multiplication to satisfy [[associativity]]. We also do not req... 16: ...t ''required'' to be associative, but associative multiplication is ''permitted''. Thus rings, which we'll call '... Empty sum (637 bytes) 5: ... simple, well known case is that 0<i>a</i> = 0 -- multiplication of any number <i>a</i> by zero always results in ... 6: ...sier to grasp than the [[empty product]] -- the [[multiplication|product]] of no numbers -- whose value is not zer... Antihomomorphism (2495 bytes) 1: ...ts with multiplication that reverses the order of multiplication. An '''antiautomorphism''' is an antihomomorphis... 3: ...map between two groups that reverses the order of multiplication. So if φ : ''X'' → ''Y'' is a group ant... 9: ...hat preserves addition, but reverses the order of multiplication. So if φ : ''X'' → ''Y'' is a ring homo... 16: Note that if the multiplication in the range of φ is [[commutative]] than an ... 18: ...up>op</sup> (which is identical to ''X'' but with multiplication reversed). Toom3 (1311 bytes) 1: '''Toom-Cook''' or '''Toom-3''' is a method of [[multiplication|multiplying]] two [[integer]]s. 25: ...oom-Cook%203-Way%20Multiplication Toom-Cook 3-Way Multiplication from GMP Documentaions] Matrix ring (548 bytes) 1: ...r [[matrix addition]] and [[matrix multiplication|multiplication]]. Vector algebra (956 bytes) 21: Multiplication of vectors and scalars obey the associative and d... 28: ...ative scalar. Division of a vector by a scalar is multiplication by the reciprocal of the scalar: Self-verifying theories (1829 bytes) 5: ...ve the [[pi-0-2 sentence]] expressing totality of multiplication:
|
|||||
|
|
|
|
|
|
Copyright 2008 WordIQ.com - Privacy Policy
::
Terms of Use
:: Contact Us
:: About Us This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "multiplication". |