Difference between revisions of "ApCoCoA-1:Num.EigenValues"
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Therefore the input matrix A has to be quadratic! | 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 | + | The output contains a matrix B. Each of the columns in B describe one of the eigenvalues of A. The first row of B contains the real part of the eigenvalues, the second row the imaginary ones. |
<example> | <example> | ||
Revision as of 14:05, 19 October 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 a matrix B. Each of the columns in B describe one of the eigenvalues of A. The first row of B contains the real part of the eigenvalues, the second row the imaginary 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([ [4077234895954899/140737488355328, -3850002255576291/281474976710656, 3186113456591853/9007199254740992, 3186113456591853/9007199254740992], [0, 0, 6871934657603045/2251799813685248, -6871934657603045/2251799813685248] ]) -------------------------------
See also
Numerical.EigenValuesAndVectors
Numerical.EigenValuesAndAllVectors
