Chiziqli operatorlar va ularning xossalari

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Chiziqli operatorlar va ularning xossalari 
 
Maxsud Tulqin o‘g’li Usmonov 
[e-mail] 
Toshkent axborot texnologiyalari universiteti Qarshi filiali 
Annotatsiya: 
Chiziqli algebra va funksional analiz fanlarining asosiy 
tushunchalaridan biri bu chiziqli operator tushunchasidir. Shu sababli ham chiziqli 
operatorlarlarni, ular aniqlangan chiziqli fazo va evklid fazolarini hamda bu fazolarda 
berilgan operatorlarlarni muhim xossalari va tatbiqlarini o`rganish juda muhim. 
Masalan, algebra fanidagi chiziqli almashtirishni, matematik fizika tenglamalari 
fanida differensiallashni operator sifatida qarash mumkin shuning uchun ham 
operator xossalarini o`rganish matematika fani nuqtayi nazaridan juda dolzarb 
masaladir.
 
Kalit so’zlar: 
Operator, chiziqli operator, operatorning matritsasi, operatorning 
rangi, nol operator, birlik operator, matritsaning xos vektori, matritsaning xos 
qiymati, xarakteristik tenglama, chiziqli operator matritsasining diagonal shakli.
 
Linear operators and their properties 
Mahsud Tulkin oglu Usmanov 
[e-mail] 
Karshi branch of Tashkent University of Information Technologies 
Abstract:
One of the basic concepts of the sciences of linear algebra and 
functional analysis is the concept of linear operator. Therefore, it is important to 
study linear operators, their defined linear spaces and Euclidean spaces, as well as the 
important properties and applications of the operators given in these spaces. For 
example, linear substitution in algebra, differentiation in mathematical physics 
equations can be considered as an operator, so the study of operator properties is very 
important from the point of view of mathematics.