2D Rotation matrices (3): recovering trigonometry from norm/orientation preservation

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 13:53

Summary:

This video discusses how, starting from the properties $R^{T}R=I$ and $det(R)=1$, we can derive the trigonometric formulas we use to “define” rotations in the plane in the video [rot2d1EN]. Therefore, these new properties could be considered as a “redefinition” of what a rotation matrix is, and indeed, this will be the case for 3D, complex vectors, or arbitrary $n$-dimensional vectors.

Using these two algebraic properties as a basis for developments is simpler than imagining what trigonometry might be like in five dimensions, for example.

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