Estimation, principal components and Hamiltonian systems
The paper advocates the use of symplectic geometry to analyzing the structure of critical points of the least squares estimation function. The problem dealt with is that of fitting a plane, in particular a line, given a data set in \({\mathbb{C}}^ n\). The basic observation is that for the fitting of a line, the least squares estimation function can be regarded as a Hamiltonian defined on the orbit of the adjoint action of the unitary group.
scientific article; zbMATH DE number 3983047
scientific article