  A particular orthogonal map on a finite dimensional real quadratic vector
space (V,Q) with a non-degenerate quadratic form Q of any signature (p,q) is
considered. It can be viewed as a correlation of the vector space that leads to
a dual Clifford algebra CL(V^*,Q) of linear functionals (multiforms) acting on
the universal Clifford algebra CL(V,Q). The map results in a unique involutive
automorphism and a unique involutive anti-automorphism of CL(V,Q). The
anti-involution reduces to reversion (resp. conjugation) for any Euclidean
(resp. anti-Euclidean) signature. When applied to a general element of the
algebra, it results in transposition of the element matrix in the left regular
representation of CL(V,Q). We give also an example for real spinor spaces. The
general setting for spinor representations will be treated in part II of this
work [...II: Spabilizer groups of primitive idempotents].
