Difference between revisions of "ApCoCoA-1:Num.EigenValuesAndVectors"

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To compute only the left hand's eigenvectors apply this method to Transposed(A).
To compute only the left hand eigenvectors apply this method to Transposed(A).

Revision as of 16:19, 22 April 2009


Computes the eigenvalues and eigenvectors of a matrix


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


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.

  • @param A A square matrix with rational entries.

  • @return 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 D both have 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 eigenvectors apply this method to Transposed(A).



-- CoCoAServer: computing Cpu Time = 0.016
  ["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

Introduction to CoCoAServer