DIDACTIC ASPECTS OF SIMPLIFYING THE ORTHOGONALIZATION PROCESS AND DEVELOPING STUDENTS’ RESEARCH ACTIVITIES
Keywords:
Euclidean space, orthogonal basis, Gram-Schmidt process, proportional modification, computational efficiency.Abstract
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.
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