st: necessity v sufficiency

[Kit Baum <baum@bc.edu>]

Al wrote

> Date: Wed, 11 Jun 2003 08:22:06 -0500
> From: "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" 
> <alan.h.feiveson@nasa.gov>
> Subject: st: RE: Re: on symmetry
>
> Kit - I don't think this works very well - consider
>
> . matrix A = (10,4,2 \ 3,10,5 \ 1,6,10)
>
> . matrix list A
>
> A[3,3]
>     c1  c2  c3
> r1  10   4   2
> r2   3  10   5
> r3   1   6  10
>
> . matrix D=A-A'
>
> . matrix list D
>
> D[3,3]
>     r1  r2  r3
> c1   0   1   1
> c2  -1   0  -1
> c3  -1   1   0
>
> . di det(D)
> 0
Many thanks to Alan for pointing out that necessity is not sufficiency 
(A-A' ==0 if symmetric), and v.v. The outtable routine (TeX from a 
Stata matrix), which made use of this flawed logic, has been revised 
(thanks to Nick Cox' noting of issym()) to handle this condition 
properly, and now only works in Stata version 8. The prior routine has 
been renamed outtable7, and warns when a matrix is assumed symmetric. 
If that is inappropriate, outtable7's nosym option will force it to 
treat the matrix as general. The outtable and outtable7 routines may be 
downloaded via ssc install outtable from SSC.

Please note that outtable(7) is complementary to statsmat of Cox and 
Baum (but may be used to output any Stata matrix, symmetric or not!)

Thanks
Kit

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