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A Theorem on Linearity
March 1968 (vol. 17 no. 3)
pp. 270-272
| ASCII Text | x | ||
| K. Doty, H. Frank, "A Theorem on Linearity," IEEE Transactions on Computers, vol. 17, no. 3, pp. 270-272, March, 1968. | |||
| BibTex | x | ||
| @article{ 10.1109/TC.1968.229100, author = {K. Doty and H. Frank}, title = {A Theorem on Linearity}, journal ={IEEE Transactions on Computers}, volume = {17}, number = {3}, issn = {0018-9340}, year = {1968}, pages = {270-272}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1968.229100}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - A Theorem on Linearity IS - 3 SN - 0018-9340 SP270 EP272 EPD - 270-272 A1 - K. Doty, A1 - H. Frank, PY - 1968 KW - Index terms?Decomposition property KW - linear KW - sequential machine KW - zero-state linearity. VL - 17 JA - IEEE Transactions on Computers ER - | |||
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. 3, pp. 270-272, March 1968, doi:10.1109/TC.1968.229100
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