Min $\text{tr} (Q^TQ)$
subject to $A^TQ+QA=C$
all the matrix is n*n matrix, the problem is to find Q such that $\text{tr} (Q^TQ)$ gets minimal value
I try to view the $A^TQ+QA=C$ as the linear transformation of Q,define the linear operator L,and try to find the adjoint operator $L^*$.$L^*$ is $AY+YA^T$ So we can use projection theorem,$Q=L^*(LL^*)^-C$ but unfortunately,I can not get the answer
Also I try to use Lagrange Multiplier method,but still can't solve Q
