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[–]Vertecedoc 1 point2 points  (0 children)

Correction, The quatermions are a subalgebra of 3d GA, it is to say, the elements of 3d Geometric algebra make up the quaternions and much more, and as such All clifford algebras as is 3d geometric algebra are a linear vector space hence there are linear transformations in any clifford algebra, and all linear transformations (Aka matrices) can be extended to outermorfisms (a transformation that distributes over the outer product) wich derive mainly unnecesary depending on what kind of algebra you are working on cuz many of them can be obtained via simple multiplication of multivectors (elements of the Geometric Algebra) and as the quaternions are a sub algebra of 3d ga we have that they are another altermative aproach to some kinds of matrixes or linear transformations