  We study $SO(m)$ covariant Matrix realizations of $ \sum_{i=1}^{m} X_i^2 = 1
$ for even $m$ as candidate fuzzy odd spheres following hep-th/0101001. As for
the fuzzy four sphere, these Matrix algebras contain more degrees of freedom
than the sphere itself and the full set of variables has a geometrical
description in terms of a higher dimensional coset. The fuzzy $S^{2k-1} $ is
related to a higher dimensional coset $ {SO(2k) \over U(1) \times U(k-1)}$.
These cosets are bundles where base and fibre are hermitian symmetric spaces.
  The detailed form of the generators and relations for the Matrix algebras
related to the fuzzy three-spheres suggests Matrix actions which admit the
fuzzy spheres as solutions. These Matrix actions are compared with the BFSS,
IKKT and BMN Matrix models as well as some others. The geometry and
combinatorics of fuzzy odd spheres lead to some remarks on the transverse
five-brane problem of Matrix theories and the exotic scaling of the entropy of
5-branes with the brane number.

High Energy Physics - Theory