A metric tensor is a second rank tensor with a contravariant rank of zero and a covariant rank of two (0,2) with the conditions:
- symmetric tensor
- determinant does not equal zero
 Sean M. Carroll, "Lecture Notes on General Relativity.", Enrico Fermi Institute, 1997, Notes
 John Stewart, "Advanced General Relativity.", Cambridge University Press (1993)
 N.M.J. Woodhouse, "General Relativity.", Springer (2006).