Gaussian noise

2014-10-27T15:49:54Z

115.249.130.58:

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Shore durometer

2013-12-18T09:57:55Z

115.249.233.122: /* Relation between ASTM D2240 hardness and elastic modulus */

{{refimprove|date=August 2012}}
In mathematics, the following [[matrix (mathematics)|matrix]] was given by [[Indian mathematics|Indian mathematician]] [[Brahmagupta]]:<ref>{{cite web |url=http://www.fq.math.ca/Scanned/34-1/suryanarayan.pdf |title=The Brahmagupta polynomials |author= |date= |work=Suryanarayanan |publisher=The Fibonacci Quarterly |accessdate=3 November 2011}}</ref>

:<math>B(x,y) = \begin{bmatrix}
x & y \\
\pm ty & \pm x \end{bmatrix}.</math>

It satisfies

:<math>B(x_1,y_1) B(x_2,y_2) = B(x_1 x_2 \pm ty_1 y_2,x_1 y_2 \pm y_1 x_2).\,</math>

Powers of the matrix are defined by

:<math>B^n = \begin{bmatrix}
x & y \\
ty & x \end{bmatrix}^n = \begin{bmatrix}
x_n & y_n \\
ty_n & x_n \end{bmatrix} \equiv B_n.</math>

The <math>\ x_n</math> and <math>\ y_n</math> are called [[Brahmagupta polynomial]]s. The Brahmagupta matrices can be extended to [[negative number|negative]] [[integer]]s:

:<math>B^{-n} = \begin{bmatrix}
x & y \\
ty & x \end{bmatrix}^{-n} = \begin{bmatrix}
x_{-n} & y_{-n} \\
ty_{-n} & x_{-n} \end{bmatrix} \equiv B_{-n}.</math>

==See also==
*[[Brahmagupta's identity]]
*[[Brahmagupta's function]]
==References==
{{reflist}}

==External links==
* Eric Weisstein. ''[http://mathworld.wolfram.com/BrahmaguptaMatrix.html Brahmagupta Matrix]'', [[MathWorld]], 1999.
*{{cite book |title=CRC Concise Encyclopedia of Mathematics |last=Weisstein |first=Eric W.|authorlink=Eric W. Weisstein|year=2003 |publisher=CRC Press |location=Florida |isbn=1-58488-347-2 |page=282}}

[[Category:Brahmagupta]]
[[Category:Matrices]]

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Gaussian noise

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