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.
Keywords :
Index terms—Decomposition property, linear, sequential machine, zero-state linearity.; Additives; Difference equations; Linear systems; Linearity; Military computing; Vectors; Index terms—Decomposition property, linear, sequential machine, zero-state linearity.;
