پديد آورنده :
پورمحمدي، شهلا
عنوان :
توان هاي هادامارد و ماتريس هاي تمام مثبت
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع. به فارسي و انگليسي
استاد راهنما :
محمود منجگاني
استاد مشاور :
فريد بهرامي
توصيفگر ها :
حاصلضرب هادامارد , ماتريس هاي تمام نامنفي , ماتريس هاي نامنفي مضاعف , ماتريس هاي مثبت مضاعف
تاريخ نمايه سازي :
23/3/94
استاد داور :
محمدرضا كوشش، مهدي نعمتي
تاريخ ورود اطلاعات :
1396/10/02
چكيده انگليسي :
Hadamard powers and totally positive matrices Mrs Shahla Pourmohamadi S pourmohamadi@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Seyed Mahmoud Manjegani Manjgani@cc iut ac irAdvisor Dr Farid Bahrami fbahrami@cc iut ac ir2007 MSC 15A15 15A48 15A57key words Conditionally positive doubly positive entry wise positive Hadamard product Hadamard power positive de nite positive matrix totally positive totally nonnegative AbstractIn this thesis we introduce and study di erent de nitions of positive matrix entry wise positive positive de nite conditionally positive and totally positive An m by n matrix A is calledtotally nonnegative positive T N T P if all minors of A are nonnegative positive We writeA T N T P if only the j by j minors where 1 j k are nonnegative positive wewrite T Nk T Pk The special in which the matrices are square in T N2 and all 2 by 2 principal minors based upon consecutive indices are positive is denoted by T N2 If A aij is anm by n entery wise nonnegative matrices then A t at denotes the Hadamard power of A ijfor any positive real number t If A B T N2 T P2 then the Hadamard product A B is aand A t for every t 0 are T N2 T P2 matrices However T Nk T Pk is not closed underHadamard multiplication when k 3 We say that entry wise nonnegative positive matrixA is eventually TN TP if there exists a T 0 such that A t is TN TP for all t T Inthis thesis also positive Hadamard powers of entery wise positive nonnegative matrices thosethat are eventually totally positiv totally nonnegative and doubly positive are charactrized Forexample for matrices with at least four rows and columns Hadamard powers greater than oneof T P matrices need not be totally positive but they are eventually positive
استاد راهنما :
محمود منجگاني
استاد مشاور :
فريد بهرامي
استاد داور :
محمدرضا كوشش، مهدي نعمتي
