Some remarks on the projector associated with the intersection of two linear manifolds
- Cite this article as:
- Taurian, O.E. & Löwdin, PO. Acta Physica (1981) 51: 5. doi:10.1007/BF03155558
The projector associated with the intersection of two linear manifolds is derived by studying the properties of the overlap matrix between the two sets spanning the linear manifolds and its adjoint matrix. The problem is reduced to an eigenvalue problem which — besides giving an explicit solution to the intersection problem — gives some additional information about the relationship between the two linear manifolds: for instance, the existence of “pairing regions” with partial overlap, and/or mutually orthogonal regions with zero overlap. Finally, an alternative approach is given which may be better suited for programming purposes.