Corrections to Glossary Entries in Halford/Wilson/Phillips TiCS paper 2010

All the italic v symbols disappeared from the glossary box on the first page of this paper in the final stages of production. Corrected versions of the glossary entries for "Inner (dot) product" and "Tensor product" appear below.

Inner (dot) product: The inner (dot) product u • v of vector u = (u₁, u₂, …, u_n) with vector v = (v₁, v₂, …, v_n) in Euclidean space is the scalar &Sigmaⁿ_i=1 u_iv_i.

Tensor product: The tensor product of two vectors u = (u₁, u₂, …, u_m) and v = (v₁, v₂, …, v_n) is a 2-subscript object similar to a matrix, B = (b_ij) where b_ij = u_iv_j. Higher rank tensor products are defined analogously, for example the product T = (t_ijk) of u, v and w = (w₁, w₂, …, w_p) would have t_ijk = u_iv_jw_k. Tensor products have several convenient mathematical properties.

Graeme S. Halford, William H. Wilson, and Steven Phillips. Relational Knowledge: The Foundation of Higher Cognition, to appear in Trends in Cognitive Sciences, 2010. Available at http://dx.doi.org/10.1016/j.tics.2010.08.005