syms b1 b2 b3 b4 b5 b6 b7
syms x11 x12 x13 x21 x23 x31 x32 x33
syms S11 S12 S22 S33 ;
B= [b1 b2 b3; b4 0 b5; b6 b7 0];
X= [x11 x12 x13 ; x21 x22 x23 ; x31 x32 x33];
C= BX + Xtranspose(B);
C1=reshape(C,9,1);
x= [x11 x12 x13 x21 x22 x23 x31 x32 x33];
The probelem is to get the co-efficient matrix A such that: A*x= 0. I have carried out the solution by hand as:
a1= [2*b1,b2,b3,b2,0,0,b3,0,0];
a2= [b4,0,0,b1,b2,b3,b5,0,0];
a3= [b6,0,0,b7,0,0,b1,b2,b3];
a4= [b4,b1,b5,0,b2,0,0,b3,0];
a5= [0,b4,0,b4,0,b5,0,b5,0];
a6= [0,b6,0,0,b7,0,b4,0,b5];
a7= [b6,b7,b1,0,0,b2,0,0,b3];
a8= [0,0,b4,b6,b7,0,0,0,b5];
a9= [0,0,b6,0,0,b7,b6,b7,0];
AA= [a1;a2;a3;a4;a5;a6;a7;a8;a9]; #the A matrix should be of this form.