I'm reading Finite Element Procedures by Bathe.
I've looked online and in the book, but couldn't find what the notation meant. To give some context, he first introduces two coordinate systems, the primed and unprimed coordinate systems. He then introduces the angle between vectors, the cross product and the definition of a scalar. Next he introduces this notation in the definition of a tensor which is as follows, (Section 2.4 page 43)
An entity is called a vector or tensor of first order if it has three components $\xi_i$ in the unprimed frame and three components $\xi_i'$ in the primed frame, and if these components are related by the characteristic law (using summation convention) $$\xi_i'=p_{ik}\xi_k$$ where $p_{ik}=\cos(\mathbf{e_i}',\mathbf{e_k})$.
My best guess is that this notation means the angle between the vectors $\mathbf{e_i}'$ and $\mathbf{e_i}$.
Thanks for any help!