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To be used for questions on geometry closely pertaining to physics. Includes differential geometry and Euclidean geometry. Do prefer the more specific tag differential-geometry for questions about differential geometry.

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Unlike rotation, why a $3\times 3$ translation matrix cannot be written in 3D? or can it be?

For example, Coxeter spends almost an entire chapter discussing the concept of Clifford translations in three-dimensional elliptic geometry in [2, Ch.VII]. … [1] Anthony Zee, Group Theory in a Nutshell for Physicists, Princeton University Press, 2016 [2] HSM Coxeter, Non-Euclidean Geometry, 5th Ed., University of Toronto Press, 1965 (First Published 1942 …
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