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A Theorem on Linearity

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2 Author(s)

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.

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Computers, IEEE Transactions on  (Volume:C-17 ,  Issue: 3 )