Difference between revisions of "ApCoCoA-1:Num.EigenValuesAndVectors"
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| − | To compute only the left hand eigenvectors apply this method to the transposed matrix of A. | + | To compute only the left hand eigenvectors apply this method to the transposed matrix of A (see <ref>Transposed</ref>). |
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<see>Num.SVD</see> | <see>Num.SVD</see> | ||
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<key>EigenValuesAndVectors</key> | <key>EigenValuesAndVectors</key> | ||
| + | <key>numerical.eigenvaluesandvectors</key> | ||
<wiki-category>Package_numerical</wiki-category> | <wiki-category>Package_numerical</wiki-category> | ||
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Revision as of 11:54, 24 April 2009
Num.EigenValuesAndVectors
Computes the eigenvalues and eigenvectors of a matrix
Syntax
Num.EigenValuesAndVectors(A:Matrix):[B:Matrix, C:Matrix, 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 numerical approximation to the eigenvalues of A 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 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
