starred and unstarred $m$ indices.

As illustrated in Fig. \[orientation\], the orientation of a spin network on the page does not affect its value. The spin network in the figure has been rotated by $180^\circ$.

As illustrated in the final diagram in Fig. \[3jnetwork\] and in Fig. \[scalarprod\], when a bra chevron and a ket chevron are juxtaposed, it represents the scalar product or contraction. In effect, the bra chevron acts as a receptacle for the ket chevron, and vice versa. After the contraction the two edges may be joined, with a small arrow remaining to indicate which was the bra and which the ket in the contraction. One might suppose that the star would carry the same information, but, as shown below, it is possible to change the direction of the arrow without changing the stars. Figure \[scalarprod\] also presents another example of Hermitian conjugation (complex conjugation, in this case). Since the small arrow represents the contraction of a bra and a ket chevron, when the chevrons are reversed, the direction of the arrow changes.

As a special case of the scalar product, the orthonormality relations of the basis vectors are illustrated in Fig. \[basison\]. The final spin network 