mf_issymmetric.hlp

是一个经济学管理应用软件 很难找的 但是经济学学生又必须用到

{smcl}
{* 21dec2004}{...}
{cmd:help mata issymmetric()}
{hline}
{* index issymmetric()}{...}
{* index issymmetriconly()}{...}
{* index symmetric matrices}{...}
{* index Hermitian matrices}{...}

{title:Title}

{p 4 8 2}
{bf:[M-5] issymmetric() -- Whether matrix is symmetric (Hermitian)}


{title:Syntax}

{p 8 12 2}
{it:real scalar}
{cmd:issymmetric(}{it:transmorphic matrix A}{cmd:)}

{p 8 12 2}
{it:real scalar}
{cmd:issymmetriconly(}{it:transmorphic matrix A}{cmd:)}


{title:Description}

{p 4 4 2}
{cmd:issymmetric(}{it:A}{cmd:)} returns 1 if {it:A}=={it:A}{bf:'} and 
returns 0 otherwise.  (Also see {cmd:mreldifsym()} in
{bf:{help mf_reldif:[M-5] reldif()}}).

{p 4 4 2}
{cmd:issymmetriconly(}{it:A}{cmd:)} returns 1 if 
{it:A}=={bf:transposeonly(}{it:A}{cmd:)} and returns 0
otherwise.


{title:Remarks}

{p 4 4 2}
{cmd:issymmetric(}{it:A}{cmd:)} and 
{cmd:issymmetriconly(}{it:A}{cmd:)} 
return the same result except when {it:A} is complex.  

{p 4 4 2}
In the complex case, {cmd:issymmetric(}{it:A}{cmd:)} returns 1 if 
{it:A} is equal to its conjugate transpose, i.e., if {it:A} is 
Hermitian,  which is the complex analog of symmetric.  
{it:A} is symmetric (Hermitian) if its off-diagonal elements are 
conjugates of each other and its diagonal elements are real.

{p 4 4 2}
{cmd:issymmetriconly(}{it:A}{cmd:)}, on the other hand, 
uses the mechanical definition of symmetry:  {it:A} is symmetriconly
{it:(sic)} if its off-diagonal elements are equal.  
{cmd:issymetriconly()} is uninteresting, mathematically speaking, but can be
useful in certain data-management programming situations.


{title:Conformability}

    {cmd:issymmetric(}{it:A}{cmd:)}, {cmd:issymmetriconly(}{it:A}{cmd:)}:
		{it:A}:  {it:r x c}
	   {it:result}:  1 {it:x} 1


{title:Diagnostics}

{p 4 4 2}
{cmd:issymmetric(}{it:A}{cmd:)} returns 0 
if {it:A} is not square.  
If {it:A} is 0 {it:x} 0, it is symmetric.

{p 4 4 2}
{cmd:issymmetriconly(}{it:A}{cmd:)} returns 0 
if {it:A} is not square.  
If {it:A} is 0 {it:x} 0, it is symmetriconly.


{title:Source code}

{p 4 4 2}
Functions are built-in.


{title:Also see}

{p 4 13 2}
Manual:  {hi:[M-5] issymmetric()}

{p 4 13 2}
Online:  help for 
{bf:{help mf_makesymmetric:[M-5] makesymmetric()}},
{bf:{help mf_reldif:[M-5] reldif()}};
{bf:{help m4_utility:[M-4] utility}}
{p_end}