matrix_symeigen.hlp

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{smcl}
{* 28mar2005}{...}
{cmd:help matrix symeigen} {right:dialog:  {bf:{dialog matrix_symeigen:matrix symeigen}}}
{hline}

{title:Title}

{p2colset 5 28 30 2}{...}
{p2col :{hi:[P] matrix symeigen} {hline 2}}Eigenvalues and eigenvectors of symmetric matrices{p_end}
{p2colreset}{...}


{title:Syntax}

{p 8 15 2}
{cmdab:mat:rix} {cmdab:syme:igen} {it:X} {it:v} {cmd:=} {it:A}


{title:Description}

{pstd}
Given an n x n symmetric matrix {it:A}, {cmd:matrix symeigen} returns the
eigenvectors in the columns of {it:X}: n x n and the corresponding eigenvalues
in {it:v}: 1 x n.  The eigenvalues are sorted from largest to smallest:
{it:v}[1,1] contains the largest eigenvalue and {it:X}[1...,1] its
corresponding eigenvector; {it:v}[1,2] contains the second largest eigenvalue
and {it:X}[1...,2] its corresponding eigenvector, and so on.

{pstd}
If you want the eigenvalues for a nonsymmetric matrix, see
{helpb matrix eigenvalues}.


{title:Examples}

{phang}{cmd:. matrix symeigen X v = A}


{title:Also see}

{psee}
Manual:  {bf:[P] matrix symeigen}

{psee}
Online:  {helpb matrix}; {helpb matrix eigenvalues}
{p_end}