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Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important appli

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse

In essence, this text is written as a challenge to others, to discover significant uses for Cayley number algebra in physics. I freely admit that though the rea

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important appli

Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equatio