Right and Left Joint System Representation of a Rational Matrix Function in General Position (System Representation Theory for Dummies)

For a rational matrix function R of one variable in general position, the matrix functions R(x)/R(y) and R(y)\R(x) of two variables are considered. For these matrix functions of two variables, representations which are analogous to the system representations (or realizations) of a rational matrix function of one variable are constructed. This representation is called the joint right [the joint left] system representation.