PROYEKTIV TEKISLIKDAGI IKKINCHI TARTIBLI CHIZIQLARNI KLASSIFIKATSIYALASH, ULARNING INVARIANTLARI VA KANONIK KO‘RINISHLARI TAHLILI
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proyektiv tekislik, konika, ikkinchi tartibli chiziq, invariant, determinant, rang, kanonik ko‘rinish, kvadratik forma, gomogen koordinatalar.Abstrak
Ushbu maqolada proyektiv tekislikdagi ikkinchi tartibli chiziqlar (konikalar)ning klassifikatsiyasi, ularning invariantlari va kanonik ko‘rinishlari o‘rganiladi. Natijalarda konikalar degeneratsiyalangan va degeneratsiyalanmagan holatlarga ajratildi, diskriminant va determinantlar asosiy invariantlar sifatida qaraldi. Shuningdek, konikalar kanonik ko‘rinishlarga keltirildi. Muhokama qismida ushbu natijalar chizma geometriya, optika va kompyuter grafikada qo‘llanishi bilan bog‘liq holda tahlil qilindi. Xulosa sifatida proyektiv invariantlar konikalarni to‘liq tavsiflash imkonini berishi ko‘rsatildi.
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