I'm sorry for this silly question. Several times I faced with optimization problems which can be expressed as
$$\begin{array}{ll} \text{minimize} & \mathrm x^T \mathrm A \mathrm x\\ \text{subject to} & \|\mathrm x\| = 1\end{array}$$
where $\mathrm A$ is square matrix and $\mathrm x$ is vector.
(This kind of problem arises in PCA or rigid alignment of 3D point sets)
I know that solution of this problem is eigenvalue decomposition of $\mathrm A$. Smallest eigenvalue should be minimum of optimization problem and corresponding eigenvector should be solution.
I want to know is there exist special name for such optimization problem?
PS: Sorry for my poor English.