Re: [R] R: determinants and inverses

From: Allan Clark <Allan.Clark_at_uct.ac.za>
Date: Tue, 22 Jan 2008 14:05:05 +0200

hello Charilaos

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

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 ).

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!!!)
>
>
>
> 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
>
>
> [[alternative HTML version deleted]]

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