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 uv of vector u = (u1, u2, …, un) with vector v = (v1, v2, …, vn) in Euclidean space is the scalar Σni=1 uivi.

Tensor product: The tensor product of two vectors u = (u1, u2, …, um) and v = (v1, v2, …, vn) is a 2-subscript object similar to a matrix, B = (bij) where bij = uivj. Higher rank tensor products are defined analogously, for example the product T = (tijk) of u, v and w = (w1, w2, …, wp) would have tijk = uivjwk. Tensor products have several convenient mathematical properties.


 

 
 
 

Copyright © Bill Wilson, 2010.
Bill Wilson's contact info

UNSW's CRICOS Provider No. is 00098G