Quaternion Function Reference

cd

Cayley-Dickson decomposition

Syntax

[A, B] = cd(q)

Description

cd returns two values which are the Cayley-Dickson components of the argument. The Cayley-Dickson form represents a quaternion as a complex number with two complex components: q = A + Bj where A = w + x i, B = y + z i. Thus: q = (w + x i) + (y + z i) j = w + xi + yj + zk. The Cayley-Dickson form of an octonion represents the octonion as a complex number with quaternion components: o = A + Bl where A and B are quaternions, and l is the octonion operator l.

Expressed in Matlab/QTFM code, A and B are such that:

q = quaternion(real(A), imag(A), real(B), imag(B)),
or in the octonion case:
o = octonion(part(A, 1), part(A, 2), part(A, 3), part(A, 4),
 part(B, 1), part(B, 2), part(B, 3), part(B, 4)).

The name of this function is the same as the MATLAB® command for changing directory, but the quaternion function is called only when the argument is a quaternion. Since a quaternion cannot designate a directory, there is no conflict.

Examples

>> q = randq
 
q = 0.01899 - 0.2061 * I - 0.9299 * J + 0.304 * K
 
>> [A, B] = cd(q)

A =  0.0190 - 0.2061i

B = -0.9299 + 0.3040i

See Also

QTFM functions: cdpolar, dc

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

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