Spinors in Three Dimensions
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High Quality Content by WIKIPEDIA articles! In mathematics, the spinor concept as specialised to three dimensions can be treated by means of the traditional notions of dot product and cross product. This is part of the detailed algebraic discussion of the rotation group SO(3). This algebra admits a convenient description, due to William Rowan Hamilton, by means of quaternions. In detail, given a vector x = (x1, x2, x3) of real (or complex) numbers, one can associate the matrix of complex numbers: {bold x}rightarrow X=left(begin{matrix}x_3&x_1-ix_2x_1+ix_2&-x_3end{matrix}right).

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High Quality Content by WIKIPEDIA articles! In mathematics, the spinor concept as specialised to three dimensions can be treated by means of the traditional notions of dot product and cross product. This is part of the detailed algebraic discussion of the rotation group SO(3). This algebra admits a convenient description, due to William Rowan Hamilton, by means of quaternions. In detail, given a vector x = (x1, x2, x3) of real (or complex) numbers, one can associate the matrix of complex numbers: {bold x}rightarrow X=left(begin{matrix}x_3&x_1-ix_2x_1+ix_2&-x_3end{matrix}right).