Quaternion Function Reference

rinv

Right inverse of octonion matrix

Syntax

X = rinv(A, B)

Description

This function computes the right inverse operator of an octonion matrix. The result, if it exists, is the octonion matrix that satisfies A * X = B. If B is omitted it defaults to an identity matrix, and X will then be the right inverse of A.

Caution: this function will yield accurate results only for small matrices, of the order of five or six rows or columns. Until a better algorithm is found, there is no way to compute an accurate inverse for a larger matrix.

Examples

>> A = rando(3)
 
A = 3x3 octonion array

>> B = rinv(A)
 
B = 3x3 octonion array
 
>> scalar(A * B)

ans =

    1.0000   -0.0000   -0.0000
   -0.0000    1.0000    0.0000
   -0.0000    0.0000    1.0000

>> abs(vector(A * B))

ans =

   1.0e-09 *

    0.0495    0.2545    0.1272
    0.0658    0.2275    0.1526
    0.0781    0.2126    0.0819

See Also

QTFM function: linv
MATLAB® function: inv

References

  1. Yongge Tian, 'Matrix representations of octonions and their applications', Advances in Applied Clifford Algebras, 10 (1), 61-90, 2000.

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

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