n = 6;
A = randn(n,n);

A = A+A';
[L, d] =ldlt(A)
L =
    1.0000         0         0         0         0         0
    0.2240    1.0000         0         0         0         0
    0.2248   27.3675    1.0000         0         0         0
    0.0756  -30.0814   -1.1436    1.0000         0         0
   -0.0650    4.7164    0.1830    0.4976    1.0000         0
   -0.2109  -17.6188   -0.6727   -0.2800    0.6164    1.0000
d =
    3.4238
    0.0764
  -54.6004
   -1.8043
   -2.1050
    1.2222
%% inertia = [3, 0, 3] 


eig(A)
ans =
   -5.6476
   -2.8218
   -0.8406
    0.3341
    2.8276
    5.2358


X =randn(n,n);
B = X'*A*X;
eig(B)
ans =
   41.8652
  -30.3999
  -14.8777
    1.4148
    0.1828
   -0.2937
[L, d] =ldlt(B);
d
d =
    6.2053
   -4.6456
   -8.7613
    3.4613
    2.5457
   -0.6464



[s,c
] = jacrot(A, 2, 4)
 [s,c
    |
{Error: Multiple left-hand sides must be separated by commas.
} 
[s,c] = jacrot(A, 2, 4)
s =
    0.3893
c =
    0.9211


help jacmeth
  function [Q, B] = jacmeth(A, nit, tol)
  jacobi's method - saves eigenvectors in Q

[Q, B] =jacmeth(A, 10, 1.e-06);
 Iter. 1 ; F-norm 3.241352e+01 
B =
    4.6882    0.9530    0.6352    0.9256   -0.0876    0.3052
    0.9530    0.3836    0.4471    0.7826    0.1701   -0.2956
    0.6352    0.4471    3.0202   -0.0812   -0.0201    0.0279
    0.9256    0.7826   -0.0812   -5.4737   -0.1062    0.0191
   -0.0876    0.1701   -0.0201   -0.1062   -2.8161         0
    0.3052   -0.2956    0.0279    0.0191   -0.0000   -0.7147
 Iter. 2 ; F-norm 6.434857e+00 
B =
    5.2317    0.1306   -0.0259   -0.0153   -0.0075    0.0420
    0.1306    0.3375   -0.0061   -0.0176   -0.0060   -0.0003
   -0.0259   -0.0061    2.8278   -0.0012   -0.0005   -0.0000
   -0.0153   -0.0176   -0.0012   -5.6475   -0.0001   -0.0000
   -0.0075   -0.0060   -0.0005   -0.0001   -2.8218    0.0000
    0.0420   -0.0003   -0.0000   -0.0000   -0.0000   -0.8403
 Iter. 3 ; F-norm 4.036246e-02 
B =
    5.2358    0.0001    0.0000    0.0000    0.0000    0.0000
    0.0001    0.3341    0.0000    0.0000   -0.0000   -0.0000
    0.0000    0.0000    2.8276    0.0000    0.0000    0.0000
    0.0000    0.0000    0.0000   -5.6476   -0.0000   -0.0000
    0.0000   -0.0000    0.0000   -0.0000   -2.8218    0.0000
    0.0000   -0.0000    0.0000   -0.0000    0.0000   -0.8406
 Iter. 4 ; F-norm 1.263946e-08 
B =
    5.2358    0.0000    0.0000    0.0000   -0.0000    0.0000
    0.0000    0.3341    0.0000    0.0000   -0.0000   -0.0000
    0.0000    0.0000    2.8276   -0.0000    0.0000    0.0000
   -0.0000    0.0000   -0.0000   -5.6476    0.0000   -0.0000
    0.0000    0.0000   -0.0000   -0.0000   -2.8218    0.0000
    0.0000   -0.0000   -0.0000   -0.0000         0   -0.8406
 Iter. 5 ; F-norm -6.770509e-15 
eig(A)
ans =
   -5.6476
   -2.8218
   -0.8406
    0.3341
    2.8276
    5.2358
diary off