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Issue No. 03 - March (1968 vol. 17)
ISSN: 0018-9340
pp: 270-272
K. Doty , IEEE
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?Decomposition property, linear, sequential machine, zero-state linearity.

K. Doty and H. Frank, "A Theorem on Linearity," in IEEE Transactions on Computers, vol. 17, no. , pp. 270-272, 1968.
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