Axborotlarga ishlov berish va boshqarish” kafedrasi tizimlarnazari ya s I fanidan Sirtqi ta’lim yo‘nalishi uchun Ma’ruza matni 5330200-«Informatika va axborot texnologiyalari»

4.7. Kelli-Gamelton teoremasi
Teorema 4.7.1. Agar kavadrat matritsa va uning c() xarakteristik ko`phadi bo`lsa, har qanday kvadrat matritsa o`zining xarakteristik tenglamasini qanoatlantiradi [8, 9].
2-tartibli matritsa uchun to`g`ridan-to`g`ri tekshirish quyidagicha amalga oshiriladi.
Xarakteristik ko`phad berilgan bo`lsin:


(4.7.1)
u holda


(4.7.2)
1. Keli-Gamelton teoremasida ko`phad elementlari darajasini pasaytirish sharti mavjud.
2. Xarakteristik ko`phad minimal ko`phadga qoldiqsiz bo`linishini tasdiqlovchi isbotga Keli-Gamelton teoremasi teng kuchlidir.
Xarakteristik tenglama dagi o`rniga matritsani qo`ysak C(A)=0 tenglama o`rinli bo`ladi, bundan matritsaning harakteristik tenglamasini quyidagicha yozamiz:


(4.7.3)
(4.7.4)


4.11-misol: C(A) topilsin,
Masalani yechish uchun quyidagi operasiya bajariladi:







Nazorat savollari.

1. 
   Matritsaga ta`rif bering.
   
2. 
   Matritsaning qanday turlari bor?
   
3. 
   Matritsalar ustida amallar bajarishda qanday xossalar o`rinli?
   
4. 
   Matritsalar ustida bajariladigan sodda amallarni misollar bilan tushuntiring.
   
5. 
   Qanday matritsa teskari matritsa deyiladi?
   

6. Matritsaning normasi qanday aniqlanadi?
7. Matritsa rangi qanday aniqlanadi?
8. Matritsaning xos soni va xos vektori qandy topiladi?
9. Texnik tizimlar bilan ishlashda matritsaning xos soni va xos vektori qanday ahamiyatga ega?
10. Kelli-Gamelton teoremasining mohiyatini tushuntiring.

1 Zadeh L.A., Desoer C.A. Linear System Theory, The State Space Approach, McGraw-Hill, N.Y., 2011, www.library.ru.

2 Artiqov A. Muhandislik texnologiyasida tahlil, kompyuterli modellashtirish va optimal yechimni topish/Darslik. Toshkent “SPEKTRUM SCOPE”, 2013 yil.

3 Ronald A. Rohrer. Introduction to Systems Theory. – Department of Electrical Engineering University of California, Berkeley, New York, 2012.

4 www.twirpx.ru, www.infanata.ru

5 Kamran Iqbal. Fundamental Engineering Optimization Methods. 1 st edition. ©2013.

6 Zadeh L.A., Desoer C.A. Linear System Theory, The State Space Approach, McGraw-Hill, N.Y., 2011.

7 Ronald A. Rohrer. Introduction to Systems Theory. – Department of Electrical Engineering University of California, Berkeley, New York, 2012.-458s.