ABSTRACT

Abstract?A system is linear if and only if it is zero-state linear, zero-input linear, and its input-output state equation has the decompostion property. In this note, it is shown that zero-state linearity is sufficient to imply that the set of states accessible from the zero state can be made into a vector space over the output field and the zeroinput response is a homomorphism on this vector space to the output space of the system. An application of the theorem to finite-state systems is given.

INDEX TERMS

Index terms?Decomposition property, linear, sequential machine, zero-state linearity.

CITATION

K. Doty, H. Frank, "A Theorem on Linearity",

*IEEE Transactions on Computers*, vol. 17, no. , pp. 270-272, March 1968, doi:10.1109/TC.1968.229100CITATIONS