  In this paper, we investigate the generalized low rank approximation to the
symmetric positive semidefinite matrix in the Frobenius norm: $$\underset{
rank(X)\leq k}{\min} \sum^m_{i=1}\left \Vert A_i - B_i XB_i^T \right
\Vert^2_F,$$ where $X$ is an unknown symmetric positive semidefinite matrix and
$k$ is a positive integer. We firstly use the property of a symmetric positive
semidefinite matrix $X=YY^T$, $Y$ with order $n\times k$, to convert the
generalized low rank approximation into unconstraint generalized optimization
problem. Then we apply the nonlinear conjugate gradient method to solve the
generalized optimization problem. We give a numerical example to illustrate the
numerical algorithm is feasible.
