  The Restricted Isometry Property (RIP) introduced by Cand\'es and Tao is a
fundamental property in compressed sensing theory. It says that if a sampling
matrix satisfies the RIP of certain order proportional to the sparsity of the
signal, then the original signal can be reconstructed even if the sampling
matrix provides a sample vector which is much smaller in size than the original
signal. This short note addresses the problem of how a linear transformation
will affect the RIP. This problem arises from the consideration of extending
the sensing matrix and the use of compressed sensing in different bases. As an
application, the result is applied to the redundant dictionary setting in
compressed sensing.
