ApCoCoA-1:Num.EigenValues: Difference between revisions
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<command> | {{Version|1}} | ||
<title> | <command> | ||
<short_description> | <title>Num.EigenValues</title> | ||
<short_description>Computes the eigenvalues of a matrix.</short_description> | |||
<syntax> | <syntax> | ||
Num.EigenValues(A:MAT):MAT | |||
</syntax> | </syntax> | ||
<description> | <description> | ||
<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 <tt>A</tt>. | |||
The | |||
<itemize> | |||
<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 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> | |||
<example> | <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]]); | 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. | -- CoCoAServer: computing Cpu Time = 0.015 | ||
------------------------------- | ------------------------------- | ||
Mat([ | Mat([ | ||
[ | ["28.970", "-13.677", "0.353", "0.353"], | ||
[ | ["0", "0", "3.051", "-3.051"] | ||
]) | ]) | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
<see>Introduction to CoCoAServer</see> | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | ||
<see> | <see>ApCoCoA-1:Num.QR|Num.QR</see> | ||
<see> | <see>ApCoCoA-1:Num.SVD|Num.SVD</see> | ||
<see> | <see>ApCoCoA-1:Num.EigenValuesAndVectors|Num.EigenValuesAndVectors</see> | ||
<see> | <see>ApCoCoA-1:Num.EigenValuesAndAllVectors|Num.EigenValuesAndAllVectors</see> | ||
</seealso> | </seealso> | ||
<wiki-category> | <types> | ||
<type>apcocoaserver</type> | |||
<type>matrix</type> | |||
</types> | |||
<key>Num.EigenValues</key> | |||
<key>EigenValues</key> | |||
<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
