A special coordinate basis of multivariable linear systems- Finite and infinite zero structure

A special coordinate basis of multivariable linear systems is introduced here. Several fundamental properties of linear systems regarding controllability (stabilisability), observability (detectability), invariant zeros, decoupling zeros, infinite zero structure, effect of feedback on zero structure, squaring down, diagonal and triangular decoupling .... etc can be directly displayed in terms of the special coordinate basis. Moreover, connections between the special coordinate basis and the important invariant subspaces of geometric theory of linear systems are established.