Matrix Representation
The algebra of the space is isomorphic to the Pauli matrix algebra such that
Matrix Representation 3D | Explicit matrix | |
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from which the null basis elements become
A general Clifford number in 3D can be written as
where the coefficients are scalar elements (including pseudoscalars). The indexes were chosen such that the representation of this Clifford number in terms of the Pauli matrices is
Read more about this topic: Paravector
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“As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.”
—Margaret Atwood (b. 1939)