<ul><li>A recent post discussed the process of embedding a 3D vector into quaternions and pulling it back out.</li><li>The embedding of a 3D vector into quaternions involves making it the vector part of a quaternion with zero real part, while returning a quaternion to 3D involves cutting off the real part.</li><li>The process includes an embedding E: ℝ3 to ℝ4 and a projection P from ℝ4 to ℝ3, with P being the transpose of E.</li><li>While P undoes what E does, E cannot recover information lost during projection, leading to discussions on left and right inverses, adjoints, and the Moore-Penrose pseudo-inverse.</li></ul>

Embeddings, Projections, and Inverses

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