Generating Orthogonal Matrices with Rational Elements

Title: Generating Orthogonal Matrices with Rational Elements

Research Question: Can we develop an algorithm to generate orthogonal matrices with rational elements?

Methodology: The researchers used the concept of stereographic projection, which is a technique used in geometry to map the surface of a sphere onto a flat surface. They applied this concept to the orthogonal matrices with rational elements.

Results: The researchers proved that each orthogonal matrix O∈SO(n,R) can be represented as a product of n(n−1)/2 matrices of elementary rotations (1.1). They also developed an algorithm for constructing orthogonal matrices over the field of rational numbers, which means that each orthogonal matrix O∈SO(n,Q) could be obtained by applying this algorithm.

Implications: This research has implications in various fields such as computer science, mathematics, and physics. It provides a new method for generating orthogonal matrices with rational elements, which can be useful in algorithms that require such matrices. Additionally, the research has potential applications in quantum mechanics and general relativity.

Link to Article: https://arxiv.org/abs/0201007v1 Authors: arXiv ID: 0201007v1