<ul><li>The map that takes a quaternion x to the quaternion qx is linear, represented as multiplication by a matrix.</li><li>The matrix representation for multiplying on the left by q is different from the matrix representation for multiplying on the right by q.</li><li>One can prove both matrix representations are correct by demonstrating their accuracy when q = 1, i, j, and k.</li><li>The post discusses how to represent rotations with quaternions and provides an equation for the equivalent rotation matrix for a rotation described by a quaternion.</li></ul>

Multiplying by quaternions on the left and right

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