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

From ApCoCoAWiki
m (replaced <quotes> tag by real quotes)
 
(9 intermediate revisions by 4 users not shown)
Line 1: Line 1:
   <command>
+
   {{Version|1}}
 +
<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>
Line 8: Line 9:
 
<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.
 
<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/>
 
<par/>
This function computes the approximate complex eigenvalues of the matrix A.
+
This function computes the approximate complex eigenvalues of the matrix <tt>A</tt>.
  
 
<itemize>
 
<itemize>
<item>@param <em>A</em> A squared matrix with rational entries.</item>
+
<item>@param <em>A</em> A quadratic matrix with rational entries.</item>
<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>
+
<item>@return The return value is a matrix with two rows. Each column of this matrix represents one approximate complex eigenvalue of <tt>A</tt>, 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>
 
</itemize>
 
   
 
   
Line 32: Line 33:
 
     </description>
 
     </description>
 
     <seealso>
 
     <seealso>
       <see>Introduction to CoCoAServer</see>
+
       <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
       <see>Numerical.QR</see>
+
       <see>ApCoCoA-1:Num.QR|Num.QR</see>
       <see>Numerical.SVD</see>
+
       <see>ApCoCoA-1:Num.SVD|Num.SVD</see>
       <see>Numerical.EigenValuesAndVectors</see>
+
       <see>ApCoCoA-1:Num.EigenValuesAndVectors|Num.EigenValuesAndVectors</see>
       <see>Numerical.EigenValuesAndAllVectors</see>
+
       <see>ApCoCoA-1:Num.EigenValuesAndAllVectors|Num.EigenValuesAndAllVectors</see>
 
     </seealso>
 
     </seealso>
 
     <types>
 
     <types>
       <type>cocoaserver</type>
+
       <type>apcocoaserver</type>
 
       <type>matrix</type>
 
       <type>matrix</type>
 
     </types>
 
     </types>
 
     <key>Num.EigenValues</key>
 
     <key>Num.EigenValues</key>
 
     <key>EigenValues</key>
 
     <key>EigenValues</key>
     <wiki-category>Package_numerical</wiki-category>
+
    <key>numerical.eigenvalues</key>
 +
     <wiki-category>ApCoCoA-1:Package_numerical</wiki-category>
 
   </command>
 
   </command>

Latest revision as of 13:47, 29 October 2020

This article is about a function from ApCoCoA-1.

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 quadratic matrix with rational entries.

  • @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.


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

See also

Introduction to CoCoAServer

Num.QR

Num.SVD

Num.EigenValuesAndVectors

Num.EigenValuesAndAllVectors