ufs_diagonalize, ufs_lagrange - diagonalize a matrix using the lagrange method

Calling sequence:

ufs_diagonalize(M)

ufs_lagrange(M)

Parameters:

M - a symmetric matrix

Synopsis:

ufs_diagonalize diagonalizes the given matrix using completion of squares (Lagrange's method).

The argument must be a symmetric matrix, otherwise an error occurs.

Example:

> A:=matrix([[2,1,0,0],[1,2,3,0],[0,3,2,1],[0,0,1,1]]);

> B:=ufs_diagonalize(A);

> L:=ufs_lagrange(A);

> C:=evalm(transpose(L) &* A &* L);