# ApCoCoA-1:Num.EigenValuesAndVectors

## Numerical.EigenValuesAndVectors

Computes the eigenvalues and eigenvectors of a matrix

### Syntax

```Num.EigenValuesAndVectors(A:Matrix):[B:Matrix, C:Matrix, D:Matrix]
```

### 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 list of three matrices, containing numerical approximation to A's eigenvalues and (right hand) eigenvectors.

The input matrix A has to be a square matrix!

The output [B:Matrix, C:Matrix, D:Matrix] contains a matrix B, where each column contains one of A's eigenvalues. The first row contains the eigenvalue's real part, the second row the imaginary. The matrices C and B have both the same dimensions as A. Column j of matrix C contains the real part of the eigenvector corresponding to eigenvalue j and column j of matrix D contains the imaginary part of the eigenvector correspsonding to eigenvalue j. To compute only the left hand's eigenvectors apply this method to Transposed(A).

#### Example

```A:=Mat([[1,2,7,18],[2,4,9,12],[23,8,9,10],[7,5,3,2]]);
Dec(Num.EigenValuesAndVectors(A),3);

-- CoCoAServer: computing Cpu Time = 0.016
-------------------------------
[Mat([
["28.970", "-13.677", "0.353", "0.353"],
["0", "0", "3.051", "-3.051"]
]), Mat([
["0.394", "-0.581", "0.260", "0.260"],
["0.435", "-0.442", "-0.547", "-0.547"],
["0.763", "0.621", "0", "0"],
["0.268", "0.281", "0.046", "0.046"]
]), Mat([
["0", "0", "-0.031", "0.031"],
["0", "0", "-0.301", "0.301"],
["0", "0", "0.680", "-0.680"],
["0", "0", "-0.274", "0.274"]
])]
--------------------------------------------------------------
```