Structure constants

Let $(𝑉, \cdot)$ be an $K$ -algebra structure on a free module with basis ${𝐞 𝑖} 𝑖 \in 𝐼$ . The structure constants $𝑐 𝑖 𝑗 𝑘$ of $𝑉$ with respect to ${𝐞 𝑖}$ are defined to be the coëfficients of the product of basis vectors expressed in that basis, #m/def/ralg i.e.

𝐞 𝑖 \cdot 𝐞 𝑗 = 𝑐 𝑖 𝑗 𝑘 𝐞 𝑘

in Einstein summation convention. Thus

(𝐯 \cdot 𝐮) 𝑘 = 𝑐 𝑖 𝑗 𝑘 𝑣 𝑖 𝑢 𝑗

#state/tidy | #lang/en | #SemBr