پديد آورنده :
احمدي، بهاره
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
هفت، [۷۹]ص.: مصور
استاد راهنما :
محمود منجگاني
استاد مشاور :
فريد بهرامي
واژه نامه :
انگليسي به فارسي; فارسي به انگليسي
توصيفگر ها :
جبر ماكس , ماتريس هاي نامنفي , مقادير ويژه , مقادير ويژه متمايز شده , قضيه نگاشت طيفي در جبر ماكس , سري هاي تواني در جبر ماكس , پيوستگي
استاد داور :
بهناز عمومي، غلامرضا اميدي
تاريخ ورود اطلاعات :
1396/10/10
چكيده انگليسي :
On the spectrum in max algebra Bahareh Ahmadi bahare ahmadi@math iut ac ir 22 11 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Seyed Mahmoud Manjgani manjgani@cc iut ac ir Advisor Dr Farid Bahrami fbahrami@cc iut ac ir 2010 MSC 15A18 15A80 Keywords Non negative matrices Max algebra Eigenvalues Distinguished eigenvalues Spectralmapping theorem in max algebra Power series in max algebra AbstractThe aim of this dissertation is introduce and study the max algebra and it s equivalance version max plus algebra We give several fundametal results of spectral theory in max algebra This includes thedescription of the spectrum of a given nonnegative matrix in max algebra with local spectral radii thespectral theorem and the spectral mapping theorem This methods enable us to obtain some relatedresults for the usual spectrum of a complex matrix in linear algebra This dissertation is written basedon article On the spectrum in max algebra V Muller and A Peperko The max algebra system consists of nonnegative real numbers R equipped with the operations ofmultiplication a b a b and maximization a b max a b for every a b R The max algebra is isomorphic to the max plus algebra which consists of the set R with operationsa b max a b and a b a b The operations extended to matrices and vectors formally in the same way as in linear algebra that is if A aij B bij and C cij are matrices with elements from R of compatible sizes we write C A B if cij aij bij for all i j C A B if cij k aik bkj maxk aik bkj for all i j and A aij for R For matrix A Rn n in the max algebra system the eigenequation for A is A x x is called max eigenvalue of and x is max eigenvectorcorresponding to Also is called the maximum circuit geometrice mean The max spectrum of Ais denoted by A R is max eigenvalue of A The max spectral radius is de ned by r A max A The max version of the Gelfand formula holds for any A Rn n i e 1 r A lim Am m m where is an arbitrary vector norm on Rn n For x Rn we de ned the local spectral radius of A in max algebra at x by 1 lim sup Ak X k rx A k The de nition of rx A is independent of the choice of norm
استاد راهنما :
محمود منجگاني
استاد مشاور :
فريد بهرامي
استاد داور :
بهناز عمومي، غلامرضا اميدي
