ApCoCoA:Num.EigenValues

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 <command>
   <title>Num.EigenValues</title>
   <short_description>Computes the eigenvalues of a matrix.</short_description>

<syntax> Num.EigenValues(A:MAT):MAT </syntax>

   <description>

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them. <par/> This function computes the approximate complex eigenvalues of the matrix A.

<itemize> <item>@param A A quadratic matrix with rational entries.</item> <item>@return The return value is a matrix with two rows. Each column of this matrix represents one approximate complex eigenvalue of A, i.e. the first entry of a column is the real part and the second entry of the same column is the imaginary part of one complex eigenvalue.</item> </itemize>


<example> Use P::=QQ[x,y,z];

A:=Mat([[1,2,7,18],[2,4,9,12],[23,8,9,10],[7,5,3,2]]); Dec(Num.EigenValues(A),3); -- CoCoAServer: computing Cpu Time = 0.015


Mat([

 [<quotes>28.970</quotes>, <quotes>-13.677</quotes>, <quotes>0.353</quotes>, <quotes>0.353</quotes>],
 [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>3.051</quotes>, <quotes>-3.051</quotes>]

])


</example>

   </description>
   <seealso>
     <see>Introduction to CoCoAServer</see>
     <see>Num.QR</see>
     <see>Num.SVD</see>
     <see>Num.EigenValuesAndVectors</see>
     <see>Num.EigenValuesAndAllVectors</see>
   </seealso>
   <types>
     <type>apcocoaserver</type>
     <type>matrix</type>
   </types>
   <key>Num.EigenValues</key>
   <key>EigenValues</key>
   <key>numerical.eigenvalues</key>
   <wiki-category>Package_numerical</wiki-category>
 </command>