BICHIZIQLI VA KVADRATIK FORMALAR
Keywords:
: bichiziqli forma, kvadratik forma, chiziqlilik, simmetrik forma, matritsa ko‘rinishi, kanonik ko‘rinish, invariantlar, diagonalizatsiya, chiziqli algebra, vektor fazosi, bilinear form, quadratic form, tasniflash, eigen qiymatlar, pozitiv aniqlik.Abstract
Ushbu mavzuda chiziqli algebra va uning umumiylashtirilgan tushunchalari hisoblangan bichiziqli va kvadratik formalar nazariyasi o‘rganiladi. Bichiziqli forma – ikki argumentli funksional bo‘lib, har bir argument bo‘yicha alohida chiziqlilik xususiyatiga ega. Kvadratik forma esa vektorlarning o‘zlari bilan bichiziqli forma orqali bog‘lanishi natijasida hosil bo‘ladigan, vektordan bitta haqiqiy sonni qaytaruvchi maxsus funksional sifatida ta’riflanadi. Mavzuda ushbu formalarni matritsa orqali ifodalash, ularning kanonik ko‘rinishga keltirilishi, invariantlar, simmetrik va nosimmetrik formalar, shuningdek, kvadratik shakllarning tasnifi kabi masalalar ko‘rib chiqiladi.
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