hello  Charilaos 
 
thank you for your reply.
 
i know how to use R to calculate the results. i want to simplify the results mathematically.
 
i found a reference that helps.
 
see mardia, kent, bibby, "multivariate analysis",  (2003) pg 457,458 for the correct simplifiations. 
 
(for those interested)
|A+BC|=|A||I(p)+inv(A)BC|=|A||I(n)+Cinv(A)B|   for B (p by n) , C (n by p), A (p by p) and non singular.
 
regards
 
 
 
Allan Clark
========
Lecturer in Statistical Sciences Department
University of Cape Town
7701 Rondebosch
South Africa
TEL (Office): +27-21-650-3228
FAX: +27-21-650-4773
http://web.uct.ac.za/depts/stats/aclark.htm 
 


>>> Charilaos Skiadas <cskiadas@gmail.com> 2008/01/22 01:24 PM >>>
Can you just multiply the matrices with %*% ( ?"%*%" ), form the  
identity through diag ( ?diag ), and then use "det" to get the  
determinant?  (though read the note in ?qr ).

Haris Skiadas
Department of Mathematics and Computer Science
Hanover College

On Jan 22, 2008, at 5:02 AM, Allan Clark wrote:

> hello all
>
> sorry for the following "none" R related question.
>
>
>
> does anyone know of a reference to calculate the following identity:
>
> |I + ABC|
>
> where I is an identity matrix and A, B,C may not have to be square  
> matrices?
>
>
> you help will be greatly appreciated.
>
>
>
> H. V. Henderson; S. R. Searle
> SIAM Review, Vol. 23, No. 1. (Jan., 1981), pp. 53-60.
>
> provides a result to calculate the inverse of I + ABC. (for those  
> interested!!!)
>
> thanking you in advance
>
>
> Allan Clark
> ========
> Lecturer in Statistical Sciences Department
> University of Cape Town
> 7701 Rondebosch
> South Africa
> TEL (Office): +27-21-650-3228
> FAX: +27-21-650-4773
> http://web.uct.ac.za/depts/stats/aclark.htm 
>
>
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