ApCoCoA-1:Num.EigenValuesAndAllVectors

Num.EigenValuesAndAllVectors

Computes eigenvalues and left and right eigenvectors of a matrix

Syntax

Num.EigenValuesAndAllVectors(A:MAT):[B:MAT, C:MAT, D:MAT, E:MAT , F: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 returns a list of five matrices, containing numerical approximation to A's eigenvalues and right and left eigenvectors.

• @param A A square matrix with rational entries.

• @return The output [B:Matrix, C:Matrix, D:Matrix, E:Matrix, F: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, D, E and F all have the same dimensions as A. Column j of matrix C contains the real part of the right eigenvector corresponding to eigenvalue j and column j of matrix D contains the imaginary part of the right eigenvector correspsonding to eigenvalue j. The matrices E and F store the left eigenvectors in the same way as C and D.

Example

A:=Mat([[1,2,7,18],[2,4,9,12],[23,8,9,10],[7,5,3,2]]); 
Dec(Num.EigenValuesAndAllVectors(A),3);
-- CoCoAServer: computing Cpu Time = 0.016
-------------------------------
[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>]
]), Mat([
  [<quotes>0.538</quotes>, <quotes>-0.600</quotes>, <quotes>0.389</quotes>, <quotes>0.389</quotes>],
  [<quotes>0.311</quotes>, <quotes>-0.222</quotes>, <quotes>-0.442</quotes>, <quotes>-0.442</quotes>],
  [<quotes>0.427</quotes>, <quotes>0.174</quotes>, <quotes>0.050</quotes>, <quotes>0.050</quotes>],
  [<quotes>0.656</quotes>, <quotes>0.748</quotes>, <quotes>0</quotes>, <quotes>0</quotes>]
]), Mat([
  [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>-0.174</quotes>, <quotes>0.174</quotes>],
  [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>0.139</quotes>, <quotes>-0.139</quotes>],
  [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>0.265</quotes>, <quotes>-0.265</quotes>],
  [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>-0.727</quotes>, <quotes>0.727</quotes>]
]), Mat([
  [<quotes>0.394</quotes>, <quotes>-0.581</quotes>, <quotes>0.260</quotes>, <quotes>0.260</quotes>],
  [<quotes>0.435</quotes>, <quotes>-0.442</quotes>, <quotes>-0.547</quotes>, <quotes>-0.547</quotes>],
  [<quotes>0.763</quotes>, <quotes>0.621</quotes>, <quotes>0</quotes>, <quotes>0</quotes>],
  [<quotes>0.268</quotes>, <quotes>0.281</quotes>, <quotes>0.046</quotes>, <quotes>0.046</quotes>]
]), Mat([
  [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>-0.031</quotes>, <quotes>0.031</quotes>],
  [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>-0.301</quotes>, <quotes>0.301</quotes>],
  [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>0.680</quotes>, <quotes>-0.680</quotes>],
  [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>-0.274</quotes>, <quotes>0.274</quotes>]
])]
-------------------------------

See also

Introduction to CoCoAServer

Num.QR

Num.SVD

Num.EigenValues

Num.EigenValuesAndVectors