For an arbitrary quantity, a,

"a" denotes a scalar quantity.

"a_i" denotes a vector.

"a_ij" denotes a 2nd-order tensor.

So, if I have something like "a_i*e_ij*b_j"

Would this be like multiplying an nx1 vector, an mxm matrix, and an Lx1 vector? It would not be a possible operation, but I'm wondering if that what it means when you multiply quantities like that.