Matrix multiplication (7683 bytes)
1: ...ves an overview of the various ways to multiply [[matrix (mathematics)|matrices]].
3: == Ordinary matrix product ==
5: ...n their '''product''' ''AB'' is an ''m''-by-''p'' matrix given by
9: ...ummarises the abstract properties of this kind of multiplication.
11: ...and ''B'' is a ''4×3'' matrix. Elements from each matrix are paired off in the direction of the arrows; ea...

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 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''²).
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:
24: \begin{matrix}
29: \end{matrix}
37: See also: [[Multiplication algorithm]], [[Binary numeral system]].

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.

Multiplication operator (471 bytes)
1: ...lize the notion of operator given by a [[diagonal matrix]].

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'':

S Matrix (8097 bytes)
1: In [[Quantum field theory]], the '''S Matrix''' is an operator mapping free particle ''in-stat...
30: The S-Matrix element must be non zero if and only if momentum ...
33: ==S-Matrix and Evolution Operator U==
48: The task is to find an expression for the S-Matrix element using the reduction formula. Before start...
89: ... a theorem that states (proof omitted) that the S-Matrix elements are the residuals of ''f'' calculated on...

(0,1)-matrix (1004 bytes)
1: ...or '''(0,1)-matrix''' is a [[matrix (mathematics)|matrix]] whose entries are all either zero or one.
7: :<math>\begin{pmatrix}
10: \end{pmatrix}</math> is a 2×2 binary matrix.
12: * A [[permutation matrix]] is a binary matrix, all of whose columns and rows each have exactly ...
13: ... matrix]] in [[analysis of variance]] is a binary matrix with constant row sums.

S matrix (1873 bytes)
1: ...S" stands for "scattering" or "Strahlung" in '''S-matrix'''.
3: ...of the [[inhomogeneous]] [[Lorentz group]]; the S-matrix is the [[evolution operator]] between time equal ...
5: ... elements (individual numerical entries) in the S-matrix are known as '''scattering amplitudes'''.
7: ... cases, the [[perturbative]] calculation of the S-matrix leads to [[Feynman diagram]]s.
11: ...ring]] for an example of the application of the S-matrix.

The Matrix (26275 bytes)
1: ... The Matrix. For other usages of the term, see [[Matrix]].''
3: [[Image:Matrix-DVD.jpg|right|The Matrix DVD case cover]]
5: '''''The Matrix''''' is a [[film]] first released in the [[United...
9: ==The Matrix series and franchise==
11: ...e provides free comics, set in the world of ''The Matrix''. Some of these comics are now available in prin...

Zero matrix (262 bytes)
1: ..., a '''zero matrix''' is a [[matrix (mathematics)|matrix]] with all its entries being zero. There are zero...

Matrix (4171 bytes)
1: ...h is ''mater''. Various disciplines use the term "matrix" with differing meanings:
5: * In [[mathematics]], a '''[[Matrix (mathematics)|matrix]]''' is a rectangular table of data.
6: * In [[computer programming]], a '''matrix''' is a 2-dimensional [[array]].
7: ...chondrion]]. See '''[[matrix (biology)|biological matrix]]'''.
8: ...nes. is called a '''[[matrix (geology)|geological matrix]]'''.

Substitution matrix (5706 bytes)
1: ...pends on the mutation rates as represented in the matrix.
21: ...construct such a matrix, called a '''substitution matrix'''. Here are the most commonly used ones:
23: == Identity Matrix ==
25: ...able to transform into any other amino acid. This matrix would look like:
27: <math>\begin{bmatrix}

The Matrix Online (3505 bytes)
1: ...d is supposed to continue the story told in the [[Matrix series]]. The game began closed beta testing in [...
3: ...action to ''[[The Matrix Reloaded]]'' and ''[[The Matrix Revolutions]]'', but it was also part of a wider ...
8: ...ethods, and special abilties. Combat is where The Matrix Online excels.
10: ...contain realistic elements of the [[Matrix series|Matrix]] storyline. However, this system is still being ...
17: ...n, but it is rumored that the characters from the Matrix movies, [[Thomas A. Anderson|Neo]] and [[Agent Sm...

Unimodular matrix (1861 bytes)
1: ...ular matrix''' is a square [[matrix (mathematics)|matrix]] with [[determinant]] +1 or -1.
3: ...which every square [[singular|non-singular]] [[submatrix]] has [[determinant]] +1, -1 or 0.
5: ...er programming|integer program]] whose constraint matrix is totally unimodular and whose right hand side i...
8: :<math>A=\begin{bmatrix}
13: \end{bmatrix}</math>

Vandermonde matrix (2678 bytes)
1: ..., a '''Vandermonde matrix''' is a [[matrix (math)|matrix]] with a [[geometric progression]] in each row, i...
3: :<math>V=\begin{bmatrix}
9: \end{bmatrix}</math>
12: ... (Some authors use the [[transpose]] of the above matrix.)
18: ...minant]] of an <math>n\times n</math> Vandermonde matrix can be expressed as follows:

Matrix exponential (14375 bytes)
1: ...dy of [[Lie group]]s and [[Lie algebra]]s, the '''matrix exponential''' is the function on square matrices...
12: ...= \begin{pmatrix} y_1(x) \\ \vdots \\y_n(x) \end{pmatrix}</math>
29: ...th ''A'', then we have a means of calculating the matrix exponential. The issue of convergence arises, whi...
32: ...e Jordan form of ''A'', with ''P'' the transition matrix. Then
48: ...x]] then ''e''^''A'' is an [[orthogonal matrix]].

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