Maths - Issue from Vassilis

By: VF_eap (vfotop1) - 2007-02-19 04:16
I'm afraid there is an other problem with the reorthogonalization procedure. 
After the symmetrical constraint for the C matrix, the article claims 
that the product of M and its transpose, is C over -2. The whole story 
afterwards is based on this "-2" for going on with the taylor approximation 
of power -1/2. 
However this is wrong. C over -1 does not imply a power of -1 (in which 
case the assumption made would be right) but the inverse matrix! So what 
should be really on the right side of the equation, should be the inverse 
of C over 2! 
Then, the aproximation should be about the square root of the M product,just 
to find the inverse of C, and finally, one more inversion to reach C. 
 
Vassilis

By: Martin Baker (martinbakerProject Admin) - 2007-02-19 08:40
Vassilis, 
 
Thanks very much, I have always been very uneasy about this derivation and I welcome a chance to sort it out. One of my problems is working out which of the rules that we use in the algebra of real numbers can safely be used in matrix algebra? 
Are you saying that the following equation is not necessarily true?: 
[C]^-1 * [C]^-1 = [C]^-2 
In the algebra of real numbers I guess the equivalent would be: 
x^-1 * x^-1 = (1/x)*(1/x) = 1/(x^2) = x^(-2) 
In other words for real numbers x^-1 is the multiplicative inverse and also works like a power. 
I think I'm missing something obvious here, or doing something silly, but I can't work out what it is. 
 
Cheers, 
 
Martin

metadata block
see also:

 

Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

cover Mathematics for 3D game Programming - Includes introduction to Vectors, Matrices, Transforms and Trigonometry. (But no euler angles or quaternions). Also includes ray tracing and some linear & rotational physics also collision detection (but not collision response).

Terminology and Notation

Specific to this page here:

 

This site may have errors. Don't use for critical systems.

Copyright (c) 1998-2017 Martin John Baker - All rights reserved - privacy policy.