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Brahmagupta Identity

Let

\begin{displaymath}
\beta\equiv \vert B\vert=x^2-ty^2,
\end{displaymath}

where $B$ is the Brahmagupta Matrix, then
$\displaystyle \mathop{\rm det} [B(x_1,y_1)B(x_2,y_2)]$ $\textstyle =$ $\displaystyle \mathop{\rm det}[B(x_1,y_1)]\mathop{\rm det}[B(x_2,y_2)]$  
  $\textstyle =$ $\displaystyle \beta_1\beta_2.$  


References

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




© 1996-9 Eric W. Weisstein
1999-05-26