Abstract / Synopsis
Hidden gems of mathematics can be recovered when one digs into what might seem an obscure text. In 1882, military officer Vidinli Hüseyin Tevfik Pasha published a book on vector algebra titled Linear Algebra. In this article we revisit the second edition of this book, emphasizing the special multiplication that we call the ’v-product’. This product has both geometric and algebraic characteristics. We attempt to clarify its relationship with complex and quaternion multiplication both geometrically and algebraically. The resulting algebra is called the Vidinli algebra. This algebra admits a Lie algebra structure that gives rise to Heisenberg algebra. We introduce a generalisation of this product: twisted v-products. Within this class of algebras the special position of the original multiplication is characterized.
DOI
10.5642/jhummath.BCUV6997
Recommended Citation
Olcay Coskun, Alp Eden & Ersin Karabudak, "Revisiting a 19th Century Vector Algebra Book," Journal of Humanistic Mathematics, Volume 15 Issue 2 (July 2025), pages 146-185. DOI: 10.5642/jhummath.BCUV6997. Available at: https://scholarship.claremont.edu/jhm/vol15/iss2/8
