(User.programs)
Item: 213 by _tasmith at hpcvbbs.UUCP
Author: [Ted A Smith]
  Subj: Eigenvalue/Eigenvector decomposition
  Keyw: eigenvalues eigenvectors functions of a matrix
  Date: Wed Feb 06 1991 22:09


Here is a quick and dirty eigenvalue/eigenvector decomposition for real
  symetric matricies.

I used the Jacobi method.

The termination test is a hack (I just test to see if the eigenvector matrix
  has changed in a given pass!) I don't have any idea if there is a possibility
  of non-termination.

Eigen takes a real symetric matrix in level 1 and returns the matrix of
  eigenvectors in level 2 and the eigenvalues are along the diagonal of the
  matrix in level 1.  (The offdiagonal values should be small in relation to
  the diagonal values.)

EClr can be used to 0 the offdiagonal values.

EFun takes a real symetric matrix (M) in level 2 and a function of 1 real arg
  (F) in level 1 and returns F(M) in level 1.

For example in analogy with 'SIN(x)^2+COS(x)^2==1':
  [[ 1 2 3 ] [ 2 4 5 ] [ 3 5 6 ]]
  DUP  \<< SIN \>> EFun DUP *
  OVER \<< COS \>> EFun DUP * +

  [[ .999999999981 9.89E-12 -1.881E-11 ]
   [ 1.188E-11 .999999999959 -3.3E-12 ]
   [ -1.801E-11 -2.3E-12 .999999999962 ]]