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Brahmagupta Matrix

A Brahmagupta matrix is defined by

B(x,y)=[x y; +/-ty +/-x].
(1)

It satisfies

B(x_1,y_1)B(x_2,y_2)=B(x_1x_2+/-ty_1y_2,x_1y_2+/-y_1x_2).
(2)

Powers of the matrix are defined by

B^n=[x y; ty x]^n
(3)
=[x_n y_n; ty_n x_n]
(4)
=B_n.
(5)

The x_n and y_n are called Brahmagupta polynomials. The Brahmagupta matrices can be extended to negative integers

B^(-n)=[x y; ty x]^(-n)
(6)
=[x_(-n) y_(-n); ty_(-n) x_(-n)]
(7)
=B_(-n).
(8)

See also

Brahmagupta Identity

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References

Suryanarayan, E. R. "The Brahmagupta Polynomials." Fib. Quart. 34, 30-39, 1996.

Referenced on Wolfram|Alpha

Brahmagupta Matrix

Cite this as:

Weisstein, Eric W. "Brahmagupta Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BrahmaguptaMatrix.html

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