MathTheBeautiful Tensors vs Space-time Numbers 4: Vector Components
184 views · Published 21 June 2017 · 10:26 · Indexed 18 October 2026
Channel: Doug Sweetser · 2017 · Science & Technology
A vector written in component form has both a magnitude and a direction expressed as a basis vector. For a vector space with an orthonormal basis, the dot product of two basis vectors will be unity if they are the same basis vector, and zero otherwise. A vector space with a non-othonormal of course be different. Space-time numbers have relationships built into the division algebra. The dot product of any two unitary space-time numbers necessarily leads to another unitary number. One good consequence is the rules for handling rotations is built right in.
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