Applications of Rational Orthogonal Matrices

The Gram–Schmidt process is a standard topic in beginning linear algebra courses. The computations, while straightforward, often require working with square roots, which can be difficult for students. We demonstrate how rational orthogonal matrices can be used to design questions examining the Gram–Schmidt method which avoid the appearance of square roots. Additionally, we show how these matrices are useful for the creation of geometry questions, which also maintain rational arithmetic. Finally, we discuss ways in which rational orthogonal matrices may be generated as well as give details of databases of generated matrices.