# 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 | + | 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 | + | 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.EigenValuesAndVectors

ApCoCoA:Numerical.EigenValuesAndAllVectors