Difference between revisions of "ApCoCoA-1:Num.EigenValues"

From ApCoCoAWiki
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   <command>
 
   <command>
 
     <title>Num.EigenValues</title>
 
     <title>Num.EigenValues</title>
     <short_description>Computes the eigenvalues of a matrix</short_description>
+
     <short_description>Computes the eigenvalues of a matrix.</short_description>
 
<syntax>
 
<syntax>
Num.EigenValues(A:Matrix):B:Matrix
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Num.EigenValues(A:MAT):MAT
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
{{ApCoCoAServer}} Please also note that you will have to use an ApCoCoAServer with enabled BLAS/LAPACK support.
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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. 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.
  
This function returns a matrix, containing numerical approximation to A's eigenvalues.  
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<itemize>
The input matrix A has to be quadratic!
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<item>@param <em>A</em> A squared matrix with rational entries.</item>
The output contains a matrix B. Each of B's columns describes one of the eigenvalues of A. The first row of B contains the real part of the eigenvalues, the second row the imaginary ones.  
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<item>@return The return value is a matrix with two rows. Each column 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>
 
<example>

Revision as of 15:13, 20 April 2009

Num.EigenValues

Computes the eigenvalues of a matrix.

Syntax

Num.EigenValues(A:MAT):MAT

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.

This function computes the approximate complex eigenvalues of the matrix A.

  • @param A A squared matrix with rational entries.

  • @return The return value is a matrix with two rows. Each column 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.


Example

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([
  ["28.970", "-13.677", "0.353", "0.353"],
  ["0", "0", "3.051", "-3.051"]
])
-------------------------------

See also

Introduction to CoCoAServer

Numerical.QR

Numerical.SVD

Numerical.EigenValuesAndVectors

Numerical.EigenValuesAndAllVectors