HOME

TheInfoList



Click Here for Items Related To - Brahmagupta Matrix
OR:
Brahmagupta Matrix on:   [Wikipedia]   [Google]   [Amazon]

In mathematics, the following
matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** '' The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...
was given by Indian mathematician
Brahmagupta Brahmagupta ( – ) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the '' Brāhmasphuṭasiddhānta'' (BSS, "correctly established doctrine of Brahma", dated 628), a theoretical tr ...
: :B(x,y) = \begin x & y \\ \pm ty & \pm x \end. It satisfies :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).\, Powers of the matrix are defined by :B^n = \begin x & y \\ ty & x \end^n = \begin x_n & y_n \\ ty_n & x_n \end \equiv B_n. The \ x_n and \ y_n are called
Brahmagupta polynomial Brahmagupta polynomials are a class of polynomials associated with the Brahmagupa matrix which in turn is associated with the Brahmagupta's identity. The concept and terminology were introduced by E. R. Suryanarayan, University of Rhode Island, Ki ...
s. The Brahmagupta matrices can be extended to negative
integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...
s: :B^ = \begin x & y \\ ty & x \end^ = \begin x_ & y_ \\ ty_ & x_ \end \equiv B_.


See also

*
Brahmagupta's identity In algebra, Brahmagupta's identity says that, for given n, the product of two numbers of the form a^2+nb^2 is itself a number of that form. In other words, the set of such numbers is closed under multiplication. Specifically: :\begin \left(a^2 + ...
* Brahmagupta's function


References


External links

* Eric Weisstein.
Brahmagupta Matrix
',
MathWorld ''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science ...
, 1999. * Brahmagupta Matrices {{math-hist-stub