Eurasian Journal of Mathematical Theory and Computer Sciences 6-jild 6-son (2026) · 12–18-betlar

DIDACTIC ASPECTS OF SIMPLIFYING THE ORTHOGONALIZATION PROCESS AND DEVELOPING STUDENTS’ RESEARCH ACTIVITIES

Ibragimov, Husniddin, Abduraxmonova, Qizlarbas

DOI: 10.5281/zenodo.20829358 · Manbada o'qish → · PDF (manba serverida)

Annotatsiya

This paper investigates the Gram-Schmidt algorithm for orthogonalizing an arbitrary basis in Euclidean space and its practical challenges. It analyzes complex fractional expressions that occur in traditional calculations, leading to increased mechanical errors among students. The paper proposes a methodology to simplify the algorithm by transforming intermediate orthogonal vectors into integer forms (proportional modification). Analysis conducted on a four-dimensional  space demonstrated that this methodology reduces algebraic confusion by up to  in practical computations and significantly improves time efficiency during lessons.

Euclidean space, orthogonal basis, Gram-Schmidt process, proportional modification, computational efficiency.Evklid fazosi, ortogonal bazis, Gramm-Shmidt jarayoni, proporsional, hisoblash samaradorligi

Metadata manbasi: jurnal OAI-PMH arxivi · Sindex to'liq matnni saqlamaydi, manbaga havola beradi.