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'' (franchis ...
was given by
Indian mathematician
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, ...
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 trea ...
:
:
It satisfies
:
Powers of the matrix are defined by
:
The
and
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:
:
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 Dig ...
, 1999.
*
Brahmagupta
Matrices
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