Entangled matrix builders

Matrices are often built and designed by applying procedures from lower order matrices. Matrix tensor products, direct sums and multiplication of matrices retain certain properties of the lower order matrices; matrices produced by these procedures are said to be {\em separable}. {\em Entangled} matrices is the term used for matrices which are not separable. Here design methods for entangled matrices are derived. These can retain properties of lower order matrices or acquire new required properties. Entangled matrices are often required in practice and a number of applications of the designs are given. Methods with which to construct multidimensional entangled paraunitary matrices are derived; these have applications for wavelet and filter bank design. New entangled unitary matrices are designed; these are used in quantum information theory. Efficient methods for designing new full diversity constellations of unitary matrices with excellent {\em quality} (a defined term) for space time applications are given.