Jacobi's rotation method

Here you have the choice:

	A 8*8 matrix with the eigenvalues +/- 10sqrt(10405) (1020.049...), the double eigenvalue 1000 and two more at 1019... and 1020, that means a cluster of dominant eigenvalues, and two more near zero: 0 and 510-100sqrt(26)=0.09805. The power method would fail here.
	The matrix representing the bending of a bar (quindiagonal) with the diagonals 1,..,1; -4,...,-4; 5,6,..,6,5; -4,...,-4; 1,...1, and the eigenvalues 16*sin(i*pi/(2(n+1)))**4, i = 1,...,n.
	Generation of a matrix from an internally stored eigensystem Rij = (sin(ij*pi/(n+1))*sqrt(2/(n+1)), i,j = 1,...,n and the eigenvalues tabulated here. Separate the numbers by blank or comma. Your input can go over several lines. For multiple values you can use the notation m*E, e.g. instead of 0,0,0,0, you write 4*0, eigenvalues chosen:
	Input of the lower triangle of a matrix (thought as symmetric). Input is rowwise, each row beginning on a new line. But a row may extend over several lines. Here also you can use the shorthand m*Z for m consecutive values Z. A =

Please choose the dimension n in the cases 2, 3 and 4
n = Important: In case 2: 3 <= n <= 30 and in cases 3,4: 2 < = n < = 30 !

Do you want printed output of the matrix A?
yes
no

Do you want printed output of the eigensystem?
yes
no

Click on "evaluate", in order to submit your input.