Difference between revisions of "ApCoCoA-1:Num.EigenValues"
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| − | <command> | + | {{Version|1}} |
| − | <title> | + | <command> |
| − | <short_description>eigenvalues of a matrix</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> | ||
| − | This function | + | <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, | + | ["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> | ||
<types> | <types> | ||
| − | <type> | + | <type>apcocoaserver</type> |
| + | <type>matrix</type> | ||
</types> | </types> | ||
| − | <key> | + | <key>Num.EigenValues</key> |
| + | <key>EigenValues</key> | ||
<key>numerical.eigenvalues</key> | <key>numerical.eigenvalues</key> | ||
| − | <wiki-category> | + | <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
