FAZODA IKKI TO’G’RI CHIZIQ ORASIDAGI MINIMAL MASOFANI TOPISHNING DETERMINANT ASOSIDAGI YONDASHUVI
Keywords:
determinant, aralash ko‘paytma, vektor ko‘paytma, minimal masofa, ayri chiziqlar, parallelepiped, invariant, fazoviy geometriya.Abstract
Ushbu maqolada fazoda ikki to‘g‘ri chiziq orasidagi minimal masofani aniqlashning determinant asosidagi yangi yondashuvi tahlil qilinadi. Klassik parametrik metodlardan farqli ravishda determinant, vektor ko‘paytma va aralash ko‘paytma invariantlariga tayangan holda masofaning ixcham analitik formulasi hosil qilindi. Tadqiqot natijasida “Transversal determinantal masofa teoremasi” deb nomlangan yangi mualliflik teoremasi isbotlandi. Ushbu teorema minimal masofa parallelepiped hajmi va parallelogramm yuzasi nisbatiga tengligini umumlashtiradi hamda koordinatalar o‘zgarishiga nisbatan to‘liq invariant ekanligini ko‘rsatadi.
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