  We prove a lower bound for Schmidt numbers of bipartite mixed states. This
lower bound can be applied easily to low rank bipartite mixed states. From this
lower bound it is known that generic low rank bipartite mixed states have
relatively high Schmidt numbers and thus entangled. We can compute Schmidt
numbers exactly for some mixed states by this lower bound as shown in Examples.
This lower bound can also be used effectively to determine that some mixed
states cannot be convertible to other mixed states by local operations and
classical communication.
  The results in this paper are proved by ONLY using linear algebra, thus the
results and proof are easy to understand.
