Quaternion Function Reference

associator

Associator

Syntax

A = associator(X, Y, Z)

Description

A = associator(X, Y, Z) returns (X * Y) * Z - X * (Y * Z). The parameters may be quaternions, octonions, or anything else that makes sense. The multiplication used is matrix multiplication. No check is made on whether the parameters are of compatible types.

Examples

Matrix multiplication is associative, so three random real matrices will produce a zero result:

>> A = randn(2); B = randn(2); C = randn(2);
>> associator(A, B, C)

ans =

   1.0e-15 *

    0.1110         0
    0.2220   -0.0555

Octonions are not associative, but quaternion-like subsets are, as shown below:

>> associator(oi, oj, ok)
 
ans = 0 * I + 0 * J + 0 * K + 0 * L + 0 * M + 0 * N + 0 * O
 
>> associator(oi, ol, oo)
 
ans = 0 * I + 2 * J + 0 * K + 0 * L + 0 * M + 0 * N + 0 * O  

Quaternions are associative, so any three chosen at random will have a zero associator.

>> associator(randq, randq, randq)
 
ans = -5.551e-17 * I + 0 * J + 1.11e-16 * K

See Also

QTFM function: commutator

References

  1. Richard D. Schafer, 'An Introduction to Non-Associative Algebras', Academic Press, 1966. Page 13.

© 2008-2013 Stephen J. Sangwine and Nicolas Le Bihan

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