Definition talk:Projection (Hilbert Spaces)

This definition seems to be overly restrictive. Any definition of a projection that I've come across is that it be an idempotent linear operator on a vector space; the definition on this page suggests that all projections are orthogonal projections (i.e. self-adjoint projections), which is obviously not the case. Nm420 17:01, 22 April 2012 (EDT)
 * Interesting. If you can find a citation for this, please post it up. One of our features of this site is that we attempt to document variants in definitions. --prime mover 18:14, 22 April 2012 (EDT)
 * At the very least, Halmos (in "Finite-dimensional vector spaces") defines a projection as an idempotent linear operator; I'm sure I've seen this definition in other texts/monographs as well, though nothing else specific comes to mind at the moment. While I could post an "alternative" definition, it seems there should just be two separate definition pages: one for a projection (an idempotent linear operator), and one for an orthogonal projection (a self-adjoint projector, which then implies the kernel and range are orthogonal). I'm hesitant to make any serious changes, though, as there are quite a few Theorem pages which assume that a projection is what I would call an orthogonal projection. Nm420 18:42, 22 April 2012 (EDT)