# ApCoCoA-1:Num.EigenValuesAndVectors

This article is about a function from ApCoCoA-1. |

## Num.EigenValuesAndVectors

Computes the eigenvalues and eigenvectors of a matrix.

### Syntax

Num.EigenValuesAndVectors(A:MAT):[B:MAT, C:MAT, 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.

This function returns a list of three matrices containing the numerical approximations of the complex eigenvalues and right eigenvectors of `A`.

@param

*A*A quadratic matrix with rational entries.@return The output is a list of three matrices

`[B:Matrix, C:Matrix, D:Matrix]`. The first matrix`B`contains the complex eigenvalues of the matrix`A`, i.e. the first entry of a column is the real part and the second entry of the same column is the imaginary part of the eigenvalue. The matrices`C`and`D`represent the right eigenvectors of`A`, i.e. the`j`-th column of`C`contains the real part of the right eigenvector corresponding to eigenvalue`j`and the`j`-th column of`D`contains the imaginary part of the same right eigenvector corresponding to eigenvalue`j`.

In order to compute the left hand eigenvectors of `A`, apply this command to the transposed matrix of `A` (see Transposed).

#### 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"] ])] --------------------------------------------------------------

### See also