factor analysis , extract second factor loading

Hi,

I have published the next post at "Analysis, Topology and Differential Geometry" but got no replays. I hope that here someone will be able to help me.

I'm trying to implement factor analysis but i cannot extract the seccund factor

I have the next correlation matrix:

1 0.9848 0.342 0 0 -0.1736

0.9848 1 0.5 0.1736 0

0.342 0.5 1 0.9397 0.866

0 0.1736 0.9398 1 0.9848

-0.1736 0 0.866 0.9858 1

I'm using simple summation method to extract the first factor loading.

and i get correct results:

0.570683029 0.704580979 0.96681105 0.821383882 0.709563721

but in the second factor i have a problem.

the book say :

make new matrix by doing so;

the entry for the correlation between T1 and T2 will be reduced by an amount to l1*l2

the example in the book is:

1-(0.572)^2, and then 1-(0.572*0.705)

(I'm Having some roundoff errors)

the first two results i get are correct but i dont know about the rest.

im continuing 1-(0.572*0.966).... and i get the next matrix

0.674320881 0.582707593 -0.209742658 -0.468749842 -0.578535974

0.582707593 0.503565644 -0.181196676 -0.40513146 -0.499945101

-0.209742658 -0.181196676 0.065276394 0.145576987 0.179985954

-0.468749842 -0.40513146 0.145676987 0.325328518 0.401975796

-0.578535974 -0.499945101 0.179985954 0.402975796 0.496519325

the sum of the first column is zero and in the book final results of the second factor loading shuld be:

-0.98211 -0.7096 0.2554 0.5707 0.7046

what i am doung wrong?