ApCoCoA-1:Num.EigenValues

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

Introduction to CoCoAServer

Num.QR

Num.SVD

Num.EigenValuesAndVectors

Num.EigenValuesAndAllVectors