05 تیر 1403
بهزاد قنبري

بهزاد قنبری

مرتبه علمی: دانشیار
نشانی:
تحصیلات: دکترای تخصصی / ریاضی کاربردی
تلفن:
دانشکده: دانشکده علوم پایه و کاربردی

مشخصات پژوهش

عنوان
A constructive method for solving the equation Xa = b in Rn: A generalization of division in Rn
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
Linear transformations; Octonions; Quaternions; Inner and cross; product of vectors
پژوهشگران بهزاد قنبری (نفر اول)، چامبونگ چان (نفر دوم)

چکیده

In this paper, we present a new approach of defining division of vectors in Rn for arbitrary dimension n. Our approach is based on constructing a class of solutions of the equation Xa = b for any two known vectors a, b ∈ Rn for arbitrary dimension n by using some basic properties of octonions. The defined procedure differs depending on the dimension of the vectors, being analyzed the cases 1 < n < 7, n = 7 and n > 7. We present an algorithm for computing divisions of vectors in multidimension space, and some numerical examples are given to confirm the presented theoretical results. Lastly, our algorithm is applied to extend several known methods of scalar case to multidimensional cases, and some numerical tests are made to compare the performance of the nonlinear system solvers.