Quaternion Function Reference

unadjoint

Unadjoint of a quaternion matrix

Syntax

C = unadjoint(A, F, B)

Description

This function reverses the result of the adjoint function, so that unadjoint(adjoint(A)) == A.

unadjoint(A) or unadjoint(A, 'complex') assumes A is a complex adjoint matrix. unadjoint(A, 'real') assumes A is a real adjoint matrix. unadjoint(A, 'quaternion') assumes A is a quaternion adjoint matrix (only valid for the case where the original matrix was a complex quaternion or biquaternion matrix). The default assumption is a complex adjoint.

The third parameter (which may appear in the second position if the second is omitted), controls the layout of the adjoint, specifically whether the adjoint is organised in blocks by components (scalar, x, y, z) or with each quaternion represented as an adjoint block. If the option 'block' was given to adjoint, then it must be given to unadjoint to reverse the effect of adjoint.

There is no opposite for 'block'. 'block' is not supported with the option 'quaternion'.

Examples

>> A = randq(2)
 
A = 2x2 quaternion array
 
>> B = unadjoint(adjoint(A))
 
B = 2x2 quaternion array
 
>> show(A - B)
 
S =
 
     0     0
     0     0

X =
 
     0     0
     0     0

Y =
 
     0     0
     0     0

Z =
 
     0     0
     0     0

See Also

QTFM function: adjoint

References

  1. F. Z. Zhang, Quaternions and Matrices of Quaternions, Linear Algebra and its Applications, 251, January 1997, 21-57. DOI: 10.1016/0024-3795%2895%2900543-9
  2. B. P. Ickes, A New Method for Performing Digital Control System Attitude Computations using Quaternions, AIAA Journal, 8(1), January 1970, pp13-17, American Institute of Aeronautics and Astronautics.
  3. Ward, J. P., Quaternions and Cayley numbers, Kluwer, 1997.
  4. Todd A. Ell, On Systems of Linear Quaternion Functions, February 2007, arXiv:math/0702084v1, http://www.arxiv.org/abs/math/0702084.
  5. Nicolas Le Bihan, Sebastian Miron and Jerome Mars, MUSIC Algorithm for Vector-Sensors Array using Biquaternions, IEEE Transactions on Signal Processing, 55(9), September 2007, 4523-4533. DOI: 10.1109/TSP.2007.896067.

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

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