Brahmagupta matrix

Brahmagupta matrix

The following matrix was given by Indian mathematician Brahmagupta in 628:Fact|date=October 2008

:B(x,y) = egin{bmatrix}x & y \pm ty & pm x end{bmatrix}.

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 = egin{bmatrix}x & y \ty & x end{bmatrix}^n = egin{bmatrix}x_n & y_n \ty_n & x_n end{bmatrix} equiv B_n.

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

:B^{-n} = egin{bmatrix}x & y \ty & x end{bmatrix}^{-n} = egin{bmatrix}x_{-n} & y_{-n} \ty_{-n} & x_{-n} end{bmatrix} equiv B_{-n}.

ee also

*Brahmagupta's identity

External links

* Eric Weisstein. " [ Brahmagupta Matrix] ", MathWorld, 1999.

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