  Outer product frames are important objects in Hilbert space frame theory. But
very little is known about them. In this paper, we make the first detailed
study of the family of outer product frames induced directly by vector
sequences. We are interested in both the quantitative attributs of these outer
product sequences (in particular, their Riesz and frame bounds), as well as
their independence and spanning properties. We show that Riesz sequences of
vectors yield Riesz sequences of outer products with the same (or better) Riesz
bounds. Equiangular tight frames are shown to produce Riesz sequences with
optimal Riesz bounds for outer products. We provide constructions of frames
which produce Riesz outer product bases with "good" Riesz bounds. We show that
the family of unit norm frames which yield independent outer product sequences
is open and dense (in a Euclidean-analytic sense) within the topological space
$ \otimes_{i=1}^M S_{N - 1}$ where $M$ is less than or equal to the dimension
of the space of symmetric operators on $\mathbb{H}^N$; that is to say, almost
every frame with such a bound on its cardinality will induce a set of
independent outer products. Thus, this would mean that finding the necessary
and sufficient conditions such that the induced outer products are dependent is
a more interesting question. For the coup de grace, we give a full analytic and
geometric classification of such sequences which produce dependent outer
products.
