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inverse of a diagonal matrix

To: <s-news@lists.biostat.wustl.edu>
Subject: inverse of a diagonal matrix
From: Stefano Sofia <stefano.sofia@usa.net>
Date: Sun, 30 Mar 2003 19:16:30 +0100
Dear Splus users,
I’ve got some problems about inverse of a symmetric matrix.
Be mymatrix a square symmetric matrix of dimension 13, with 
0.51 in the diagonal
-0.04636364 everywhere else.
Within the library Matrix, the command solve(mymatrix) gives back the inverse
of mymatrix. But I realised that the output of solve is not the correct matrix
at all; first of all the output is not a symmetric matrix, and multiplying
mymatrix with this presumed inverse I get a matrix far from being the identity
matrix.
The determinant of mymatrix is very small (1.31649e-019) but still recognised
as greater than zero. Is that possible to improve the precision of the
calculations or the smallness of the determinant makes any improvement
impossible?
Am I using the right method for the inverse?


I’m using Splus4 in a Windows XP environment.
Any help will be greatly appreciated
Stefano



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