  A superposition of a matrix ensemble refers to the ensemble constructed from
two independent copies of the original, while a decimation refers to the
formation of a new ensemble by observing only every second eigenvalue. In the
cases of the classical matrix ensembles with orthogonal symmetry, it is known
that forming superpositions and decimations gives rise to classical matrix
ensembles with unitary and symplectic symmetry. The basic identities expressing
these facts can be extended to include a parameter, which in turn provides us
with probability density functions which we take as the definition of special
parameter dependent matrix ensembles. The parameter dependent ensembles
relating to superpositions interpolate between superimposed orthogonal
ensembles and a unitary ensemble, while the parameter dependent ensembles
relating to decimations interpolate between an orthogonal ensemble with an even
number of eigenvalues and a symplectic ensemble of half the number of
eigenvalues. By the construction of new families of biorthogonal and skew
orthogonal polynomials, we are able to compute the corresponding correlation
functions, both in the finite system and in various scaled limits. Specializing
back to the cases of orthogonal and symplectic symmetry, we find that our
results imply different functional forms to those known previously.
