Brahmagupta matrix explained

In mathematics, the following matrix was given by Indian mathematician Brahmagupta:^[1]

B(x,y) = \begin{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} = \begin{bmatrix} x & y \\ ty & x \end{bmatrix} ^{n} = \begin{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} = \begin{bmatrix} x & y \\ ty & x \end{bmatrix} ^{-n} = \begin{bmatrix} x _{-n} & y _{-n} \\ ty _{-n} & x _{-n} \end{bmatrix} \equiv B _{-n} .

See also

• Brahmagupta's identity
• Brahmagupta's function

External links

• Eric Weisstein. Brahmagupta Matrix, MathWorld, 1999.
• Book: Weisstein, Eric W.. Eric W. Weisstein

. CRC Concise Encyclopedia of Mathematics . Eric W. Weisstein. 2003 . CRC Press . Florida . 1-58488-347-2 . 282.

Notes and References

1. Web site: The Brahmagupta polynomials . Suryanarayanan . The Fibonacci Quarterly . 3 November 2011.