Hello. 

 You reversed my correction related to ORTHONORMAL matrices. 

 I think you should do some research or consult true mathematicians.  In physics as in econometrics, it is a habit to call orthogonal matrices which are really orthonormal.  This is because they usually work with normalized vectors or automatically normalize vectors and matrices.  But the true mathematical definitions differ as a perfectly orthogonal matrix, which is not normalized is NOT its transpose-inverse. 

 Simple example: 

 A = [1,2 / -2,1], is ORTHOGONAL and its transpose is At = [1,-2 /2,1]  
 BUT:   A.At = [5,0 / 0,5] is obviously not the identity matrix.   

 There atre two different names because there are two different objects. 

 Physicists and economists may call it what they want, but in mathemetics, orthogonal does not mean orthonormal. 

 raphaelcohen@xplornet.com