mf_conj.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}
{* 18mar2005}{...}
{cmd:help mata conj()}
{hline}
{* index conj()}{...}
{* index conjugate}{...}
{* index conjugate transpose}{...}
{* index adjoint matrix}{...}
{* index adjugate matrix}{...}
{* index Hermitian adjoin}{...}
{* index Hermitian transpose}{...}

{title:Title}

{p 4 4 2}
{bf:[M-5] conj() -- Complex conjugate}


{title:Syntax}

{p 8 12 2}
{it:numeric matrix}
{cmd:conj(}{it:numeric matrix Z}{cmd:)}


{title:Description}

{p 4 4 2}
{cmd:conj(}{it:Z}{cmd:)} returns the elementwise complex conjugate of 
{it:Z}, i.e., {cmd:conj(}{it:a}+{it:b}i{cmd:)} = {it:a}-{it:b}i.
{cmd:conj()} may be used with real or complex matrices.  If {it:Z} is 
real, {it:Z} is returned unmodified.


{title:Remarks}

{p 4 4 2}
Note that, given {it:m} {it:x} {it:n} matrix {it:Z}, {cmd:conj(}{it:Z}{cmd:)}
returns an {it:m} {it:x} {it:n} matrix; it does not return the transpose.  To
obtain the conjugate transpose matrix, also known as the adjoint matrix,
adjugate matrix, Hermitian adjoin, or Hermitian transpose, code

		{it:Z}{cmd:'}

{p 4 4 2}
See {bf:{help m2_op_transpose:[M-2] op_transpose}}.

{p 4 4 2}
A matrix equal to its conjugate transpose is called Hermitian or self-adjoint
although, in this manual, we often use the term symmetric.


{title:Conformability}

    {cmd:conj(}{it:Z}{cmd:)}:
		{it:Z}:  {it:r x c}
	   {it:result}:  {it:r x c}


{title:Diagnostics}

{p 4 4 2}
{cmd:conj(}{it:Z}{cmd:)} returns a real matrix if {it:Z} is real and a complex
matrix if {it:Z} is complex.

{p 4 4 2}
{cmd:conj(}{it:Z}{cmd:)}, if {it:Z} is real, 
returns {it:Z} itself and not a copy.  This makes {cmd:conj()} execute 
instantly when applied to real matrices.


{title:Source code}

{p 4 4 2}
Function is built-in.


{title:Also see}

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

{p 4 13 2}
Online:  help for 
{bf:{help mf__transpose:[M-5] _transpose}};
{bf:{help m4_scalar:[M-4] scalar}}
{p_end}