KUB MATRITSALARDA KO‘PAYTIRISH AMALLARINI BAJARISH HAQIDA
Keywords:
Kalit so‘zlar: Kub matritsa, uch o‘lchamli massiv, kvadratik stoxastik jarayonlar, Markov jarayoni, Maksimov ko‘paytma amali, Kolmogorov–Chapman tenglamasi, algebraik tuzilma, chiziqli algebra, tenzor tahlili., Keywords: cubic matrix, three-dimensional array, quadratic stochastic processes, Markov process, Maksimov multiplication operation, Kolmogorov–Chapman equation, algebraic structure, linear algebra, tensor analysis.Abstract
Annotatsiya. Ushbu maqolada kub matritsalar tushunchasi, ularning algebraik xossalari va ko‘paytirish amalining nazariy asoslari ko‘rib chiqilgan. Uch o‘lchamli matritsa elementlari o‘rtasidagi o‘zaro bog‘liqlik, ularning matematik modellashtirish va amaliy qo‘llashdagi ahamiyati tahlil qilingan. Shuningdek, kub matritsalar ko‘paytmasini aniqlashda qo‘llaniladigan formulalar va ularning chiziqli algebra hamda tenzor tahlil bilan aloqasi ochib berilgan.
Abstract. This article explores the concept of cubic matrices, their algebraic properties, and the theoretical foundations of the multiplication operation. The interrelations among the elements of three-dimensional matrices, as well as their significance in mathematical modeling and practical applications, are analyzed. In addition, the formulas used to determine the product of cubic matrices and their connections with linear algebra and tensor analysis are presented.
