# ApCoCoA-1:Num.EigenValues

## Numerical.EigenValues

eigenvalues of a matrix

### Syntax

$numerical.EigenValues(A:Matrix):List

### 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. Please also note that you will have to use an ApCoCoAServer with enabled BLAS/LAPACK support.

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