  A natural family of quantized matrix algebras is introduced. It includes the
two best studied such. Located inside ${\s U}_q(A_{2n-1})$, it consists of
quadratic algebras with the same Hilbert series as polynomials in $n^2$
variables. We discuss their general properties and investigate some members of
the family in great detail with respect to associated varieties, degrees,
centers, and symplectic leaves. Finally, the space of rank r matrices becomes a
Poisson submanifold, and there is an associated tensor category of $\rank\leq
r$ matrices.
