Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In projective geometry and linear algebra, the projective orthogonal group PO is the induced action of the orthogonal group of a quadratic space V = (V,Q)[note 1] on the associated projective space P(V). Explicitly, the projective orthogonal group is the quotient group PO(V) = O(V)/ZO(V) = O(V)/{±I} where O(V) is the orthogonal group of (V) and ZO(V)={±I} is the subgroup of all orthogonal scalar transformations of V – these consist of the identity and reflection through the origin. These scalars are quotiented out because they act trivially on the projective space and they form the kernel of the action, and the notation "Z" is because the scalar transformations are the center of the orthogonal group. The projective special orthogonal group, PSO, is defined analogously, as the induced action of the special orthogonal group on the associated projective space.

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