however by $\sqrt{2j+1}$ because of a normalization convention. Figure \[2jnetwork\] shows first the spin network for the components of $K$, which is conceived of as a standard bivalent node or intertwiner. The small arrows indicate that the components on the first line can be considered the result of plugging basis kets into the intertwiner itself, as seen on the second line. The short line extending above the node is a “stub” (Stedman 1990), whose purpose is to orient the node. The convention is that if we start at the stub and move in a positive (counterclockwise) direction, the first and second edges we encounter are respectively the first and second operands of $K$, conceived of as a map $:\CS_j\otimes\CS'_j\to\Complexes$.

We note that if $V$ and $W$ are vector spaces, then $V\times W$ is not the same as $V\otimes W$, but if we have a bilinear map on $V \times
W$ it can be extended to a linear map on $V\otimes W$ by linear superposition. For example, in the previous paragraph we have regarded $K$ as a bilinear map $:\CS_j \times \CS'_j\to\Complexes$, and computed its components as $K(\ket{jm},\ket{jm'})$. The first and second operands of this expression correspond to the first and 