Solve Function Doesn't Give All Solutions

% this does not give all the solutions
A = [0.7 0.2;
    0.05 0.64];
C = [0.5 -0.8;
    0 0.7];
Q = [0.5 0;
    0 0.7];
R = [1 0;
    0 0.8];
T = sym('T',[2 2]);
L = sym('L',[2 2]);
[Pba,L2,G] = dare(A',C',Q,R);
P = C*Pba*C'+R;
f = trace(P^(-1)*(T*P*T'+L-P));
x = solve(f,[T,L])

The answer(solution) is like that:

x = 
struct with fields:
T1_1: 0
T2_1: 0
T1_2: 0
T2_2: 0
L1_1: 1298074214633706853141718390451145/425558238297866865348786096439296
L2_1: 0
L1_2: 0
L2_2: 0

However, there are other solutions, such as T=[1,0;0,1], L=[0,0;0,0];

Why does the code not give me all the reasonable solutions for T and L？

Thanks！

Answer 1

[Torsten]

Using

x = solve(f,[T,L],'ReturnConditions',1)

instead of

x = solve(f,[T,L])

might help.

[Joey Qi]

Yes, it works. Thanks, Torsten!