# Difference between revisions of "ApCoCoA-1:Num.EigenValues"

From ApCoCoAWiki

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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||

<par/> | <par/> | ||

− | This function computes the approximate complex eigenvalues of the matrix A. | + | This function computes the approximate complex eigenvalues of the matrix <tt>A</tt>. |

<itemize> | <itemize> | ||

− | <item>@param <em>A</em> A | + | <item>@param <em>A</em> A quadratic matrix with rational entries.</item> |

− | <item>@return The return value is a matrix with two rows. Each column represents one approximate complex eigenvalue of 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 one complex eigenvalue.</item> | + | <item>@return The return value is a matrix with two rows. Each column of this matrix represents one approximate complex eigenvalue of <tt>A</tt>, 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 one complex eigenvalue.</item> |

</itemize> | </itemize> | ||

## Revision as of 14:27, 7 July 2009

## Num.EigenValues

Computes the eigenvalues of a matrix.

### Syntax

Num.EigenValues(A:MAT):MAT

### 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 computes the approximate complex eigenvalues of the matrix `A`.

@param

*A*A quadratic matrix with rational entries.@return The return value is a matrix with two rows. Each column of this matrix represents one approximate complex eigenvalue of

`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 one complex eigenvalue.

#### Example

Use P::=QQ[x,y,z]; A:=Mat([[1,2,7,18],[2,4,9,12],[23,8,9,10],[7,5,3,2]]); Dec(Num.EigenValues(A),3); -- CoCoAServer: computing Cpu Time = 0.015 ------------------------------- Mat([ [<quotes>28.970</quotes>, <quotes>-13.677</quotes>, <quotes>0.353</quotes>, <quotes>0.353</quotes>], [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>3.051</quotes>, <quotes>-3.051</quotes>] ]) -------------------------------

### See also