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