ABOUT BIJECTIVITY OF TRANSFORMATIONS DETERMINED BY QUASI-HADAMARD MATRIXES
( Pp. 6-13)
More about authors
Litvinenko Vitaly Sergeevich
sotrudnik FGUP «NII «KVANT»
Federal State Unitary Enterprise Scientific Research Institute KVANT Nikonov Vladimir G. Doctor of Engineering, Professor; member at the Presidium
Russian Academy of Natural Sciences
Moscow, Russian Federation
Federal State Unitary Enterprise Scientific Research Institute KVANT Nikonov Vladimir G. Doctor of Engineering, Professor; member at the Presidium
Russian Academy of Natural Sciences
Moscow, Russian Federation
Abstract:
The article continues studies of bijective mapping determined by quasi-hadamard matrixes started in [НЛ15]. It is proved that if mapping determined by quasi-hadamard martixes $A_{n}$ is bijective, then the inverse mapping is set by the transposed matrix $A_{T}^n$. It is also proved that any quasi-hadamard matrix of order 4, 6 or 8 determines bijective coordinate-threshold map.
How to Cite:
Litvinenko V.S., Nikonov V.G., (2016), ABOUT BIJECTIVITY OF TRANSFORMATIONS DETERMINED BY QUASI-HADAMARD MATRIXES. Computational Nanotechnology, 1 => 6-13.
Reference list:
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GS67 Goethals, J.M., and Seidel, J.J. Orthogonal matrices with zero diagonal. 1967. Canadian Journal of Mathematics, vol. 19, pp. 1001-1010.
GEN03 Glukhov M.M., Elizarov V.P., Nechaev A.A. Algebra. 2003. T. 1, 2.
Der67 Dertouzos M. Porogovaya logika, 1967.
NL15 Nikonov V.G., Litvinenko V.S. Geometricheskiy podkhod k dokazatel stvu biektivnosti odnogo koordinatno-porogovogo otobrazheniya // Computational nanotechnology. 2015. №4. S. 26-30.
NS03 Nikonov V.G., Sarantsev A.V. Metody kompaktnoy realizatsii biektivnykh otobrazheniy, zadannykh regulyarnymi sistemami odnotipnykh bulevykh funktsiy // Vestnik Rossiyskogo universiteta druzhby narodov. Seriya: Prikladnaya i komp yuternaya matematika. 2003. T. 2. № 1. S. 94-105.
NS04 Nikonov V.G., Sarantsev A.V. Postroenie i klassifikatsiya regulyarnykh sistem odnotipnykh funktsiy // Informatsionnye tekhnologii v nauke, obrazovanii, telekommunikatsii i biznese: materialy XXXI Mezhdunarodnoy konferentsii. T. 5 iz Pril. 1. - M.: Akademiya estestvoznaniya, 2004. S. 173-174.
NS09 Nikonov V.G., Sidorov E.S. O sposobe postroeniya vzaimno odnoznachnykh otobrazheniy pri pomoshchi kvaziadamarovykh matrits // Vestnik Moskovskogo gosudarstvennogo universiteta lesa - Lesnoy vestnik. 2009. №2 (65).
GS67 Goethals, J.M., and Seidel, J.J. Orthogonal matrices with zero diagonal. 1967. Canadian Journal of Mathematics, vol. 19, pp. 1001-1010.
GEN03 Glukhov M.M., Elizarov V.P., Nechaev A.A. Algebra. 2003. T. 1, 2.
Der67 Dertouzos M. Porogovaya logika, 1967.
NL15 Nikonov V.G., Litvinenko V.S. Geometricheskiy podkhod k dokazatel stvu biektivnosti odnogo koordinatno-porogovogo otobrazheniya // Computational nanotechnology. 2015. №4. S. 26-30.
NS03 Nikonov V.G., Sarantsev A.V. Metody kompaktnoy realizatsii biektivnykh otobrazheniy, zadannykh regulyarnymi sistemami odnotipnykh bulevykh funktsiy // Vestnik Rossiyskogo universiteta druzhby narodov. Seriya: Prikladnaya i komp yuternaya matematika. 2003. T. 2. № 1. S. 94-105.
NS04 Nikonov V.G., Sarantsev A.V. Postroenie i klassifikatsiya regulyarnykh sistem odnotipnykh funktsiy // Informatsionnye tekhnologii v nauke, obrazovanii, telekommunikatsii i biznese: materialy XXXI Mezhdunarodnoy konferentsii. T. 5 iz Pril. 1. - M.: Akademiya estestvoznaniya, 2004. S. 173-174.
NS09 Nikonov V.G., Sidorov E.S. O sposobe postroeniya vzaimno odnoznachnykh otobrazheniy pri pomoshchi kvaziadamarovykh matrits // Vestnik Moskovskogo gosudarstvennogo universiteta lesa - Lesnoy vestnik. 2009. №2 (65).
Keywords:
bijective mapping, threshold function, quasidemocracy matrix.
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