Some Identities involving Two Sets of Basis Vectors and the Metric and   Mixed Matrices
  Given two sets of basis vectors in n-dimensional space, there exists a relation between their lengths and mutual angles, expressed as relations between the two metric matrices and the mixed matrix. In this paper these relations are given, and their consequences for 2-dimensional and 3-dimensional space are investigated, using a computer algebra program for simplifying expressions. 
M.J. Kronenburg
math.RA