Brahmagupta matrix

In mathematics, the following matrix was given by Indian mathematician Brahmagupta:

$B(x,y)=\left[\begin{array}{cc}x& y\\ \pm ty& \pm x\end{array}\right].$

It satisfies

$B(x_1,y_1)B(x_2,y_2)=B(x_1{x}_2\pm t{y}_1{y}_2,x_1{y}_2\pm y_1{x}_2).$

Powers of the matrix are defined by

$B^n={\left[\begin{array}{cc}x& y\\ ty& x\end{array}\right]}^n=\left[\begin{array}{cc}{x}_n& y_n\\ t{y}_n& x_n\end{array}\right]\equiv B_n.$

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

$B^{-n}={\left[\begin{array}{cc}x& y\\ ty& x\end{array}\right]}^{-n}=\left[\begin{array}{cc}{x}_{-n}& y_{-n}\\ t{y}_{-n}& x_{-n}\end{array}\right]\equiv B_{-n}.$

See also

• Brahmagupta's identity
• Brahmagupta's function

External links

• Eric Weisstein. Brahmagupta Matrix, MathWorld, 1999.
• Weisstein, Eric W. (2003). CRC Concise Encyclopedia of Mathematics. Florida: CRC Press. p. 282. ISBN 1-58488-347-2.