DocumentCode
1190304
Title
A Theorem on Linearity
Author
Doty, K. ; Frank, H.
Author_Institution
IEEE
Issue
3
fYear
1968
fDate
3/1/1968 12:00:00 AM
Firstpage
270
Lastpage
272
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.;
fLanguage
English
Journal_Title
Computers, IEEE Transactions on
Publisher
ieee
ISSN
0018-9340
Type
jour
DOI
10.1109/TC.1968.229100
Filename
1687329
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