Английская Википедия:Brahmagupta matrix

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Шаблон:More citations needed In mathematics, the following matrix was given by Indian mathematician Brahmagupta:

<math>B(x,y) = \begin{bmatrix}

x & y \\ \pm ty & \pm x \end{bmatrix}.</math>

It satisfies

<math>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).\,</math>

Powers of the matrix are defined by

<math>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.</math>

The <math>\ x_n</math> and <math>\ y_n</math> are called Brahmagupta polynomials. The Brahmagupta matrices can be extended to negative integers:

<math>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}.</math>

See also

• Brahmagupta's identity
• Brahmagupta's function

External links

• Eric Weisstein. Brahmagupta Matrix, MathWorld, 1999.
• Шаблон:Cite book

Шаблон:Matrix-stub Шаблон:Math-hist-stub