ApCoCoA-1:Num.SimDiag

Num.SimDiag

Computes an approximate diagonalization of a set of matrices.

Syntax

Num.SimDiag(A:LSIT):[B:MAT, C: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 two matrices, containing the approximate (almost) eigenvectors of the matrices in A and its inverse.

• @param A A list of quadratic matrices with rational entries.

• @return The output is a list of two matrices [B:MAT, C:MAT]. The first matrix B contains the real almost eigenvectors of the matrices in A. The matrix C is the inverse of A.

Example

M1 := Mat([[0, 0, -0.079, -0.018],[0, 0,  0.032, -0.012], [1, 0,  1.056, -0.012],[0, 1, -0.060,  1.025]]);
M2 := Mat([[0, -0.063, 0, -0.018],[1,  1.026, 0, -0.012], [0, 0, 0, -0.012], [0, 0, 1, 1.025]]);
M1 := Transposed(M1);
M2 := Transposed(M2);
Result := Num.SimDiag([M1,M2],10);

Dec(Result[2]*M1*Result[1],3);
Dec(Result[2]*M2*Result[1],3);

Mat([
  [<quote>0.062</quote>, <quote>0.016</quote>, <quote>0.000</quote>, <quote>0.006</quote>],
  [<quote>0.021</quote>, <quote>0.030</quote>, <quote>-0.002</quote>, <quote>-0.000</quote>],
  [<quote>0.000</quote>, <quote>0.005</quote>, <quote>1.006</quote>, <quote>-0.035</quote>],
  [<quote>-0.000</quote>, <quote>-0.000</quote>, <quote>-0.031</quote>, <quote>0.982</quote>]
])
-------------------------------
Mat([
  [<quote>0.048</quote>, <quote>0.000</quote>, <quote>0.030</quote>, <quote>-0.005</quote>],
  [<quote>0.000</quote>, <quote>0.991</quote>, <quote>-0.002</quote>, <quote>-0.021</quote>],
  [<quote>0.020</quote>, <quote>0.005</quote>, <quote>0.029</quote>, <quote>-0.000</quote>],
  [<quote>0.000</quote>, <quote>-0.030</quote>, <quote>-0.000</quote>, <quote>0.982</quote>]
])

See also

Introduction to CoCoAServer

Num.QR

Num.SVD

Num.EigenValues

Num.EigenValuesAndVectors

Num.EigenValuesAndAllVectors