R help - Oct 2011 - symmetric matrix multiplication

I have a symmetric matrix B (17x17), and a (17x17) square matrix A.  If do
the following matrix multiplication I SHOULD get a symmetric matrix, however
i don't.  The computation required is:

C = t(A)%*%B%*%A

here are some checks for symmetry
> (max(abs(B - t(B))))
[1] 0
> C = t(A)%*%B%*%A
> (max(abs(C - t(C))))
[1] 3.552714e-15

Any help on the matter would be very much appreciated.


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> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at
r-project.org]
> On Behalf Of statfan
> Sent: Saturday, October 22, 2011 10:45 PM
> To: r-help at r-project.org
> Subject: [R] symmetric matrix multiplication
> 
> I have a symmetric matrix B (17x17), and a (17x17) square matrix A.  If do
> the following matrix multiplication I SHOULD get a symmetric matrix,
> however
> i don't.  The computation required is:
> 
> C = t(A)%*%B%*%A
> 
> here are some checks for symmetry
> > (max(abs(B - t(B))))
> [1] 0
> > C = t(A)%*%B%*%A
> > (max(abs(C - t(C))))
> [1] 3.552714e-15
> 
> Any help on the matter would be very much appreciated.
> 
> 
Welcome to the world of floating-point calculation on finite precision
computers.  You need to read R FAQ 7.31.  Your maximum difference is for all
intents and purposes equal to zero.

Hope this is helpful,

Dan

Daniel Nordlund
Bothell, WA USA