Difference between revisions of "ApCoCoA:Num.EigenValues"

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     <description>
 
     <description>
 
This function returns a matrix, containing numerical approximation to A's eigenvalues.  
 
This function returns a matrix, containing numerical approximation to A's eigenvalues.  
Therefore the input matrix A has to be rectangular!
+
Therefore the input matrix A has to be quadratic!
 
It is implemented in the ApCoCoA server, so you need a running server. It was not implemented in version 0.99.4 or previous. Also please keep in mind this method is based on blas/Lapack's eigenvalue solver and uses floating point arithmetic. This is not an exact, algebraic method!
 
It is implemented in the ApCoCoA server, so you need a running server. It was not implemented in version 0.99.4 or previous. Also please keep in mind this method is based on blas/Lapack's eigenvalue solver and uses floating point arithmetic. This is not an exact, algebraic method!
The output contains of a matrix B, where the number of rows contains one of A's eigenvalues. The first column contains the eigenvalue's real part, the second the imaginary.
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The output contains of a matrix B. Each of the rows in B describe on of the eigenvalues of A. The first column of B contains the real part of the eigenvalues, the second column the imagonary ones.  
 +
 
 
<example>
 
<example>
 
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]]);

Revision as of 09:55, 17 September 2008

Numerical.EigenValues

eigenvalues of a matrix

Syntax

$numerical.EigenValues(A:Matrix):List

Description

This function returns a matrix, containing numerical approximation to A's eigenvalues.

Therefore the input matrix A has to be quadratic!

It is implemented in the ApCoCoA server, so you need a running server. It was not implemented in version 0.99.4 or previous. Also please keep in mind this method is based on blas/Lapack's eigenvalue solver and uses floating point arithmetic. This is not an exact, algebraic method! The output contains of a matrix B. Each of the rows in B describe on of the eigenvalues of A. The first column of B contains the real part of the eigenvalues, the second column the imagonary ones.

Example

A:=Mat([[1,2,7,18],[2,4,9,12],[23,8,9,10],[7,5,3,2]]);
Numerical.EigenValues(A);
-- CoCoAServer: computing Cpu Time = 0.0049
-------------------------------
Mat([
  [2038617447977453/70368744177664, 1593056728295919/4503599627370496, 0, 1717983664400761/562949953421312],
  [-3850002255576293/281474976710656, 1593056728295919/4503599627370496, 0, -1717983664400761/562949953421312]
])
-------------------------------

See also

ApCoCoA:Introduction to CoCoAServer

ApCoCoA:Numerical.QR

ApCoCoA:Numerical.SVD

ApCoCoA:Numerical.EigenValuesAndVectors

ApCoCoA:Numerical.EigenValuesAndAllVectors