A contravariant tensor is a Tensor having specific transformation properties (c.f., a Covariant Tensor). To
examine the transformation properties of a contravariant tensor, first consider a Tensor of Rank 1 (a Vector)
Covariant Tensors are a type of Tensor with differing transformation properties, denoted
. However, in 3-D Cartesian Coordinates,
To turn a Covariant Tensor into a contravariant tensor, use the Metric Tensor to write
See also Covariant Tensor, Four-Vector, Lorentz Tensor, Metric Tensor, Mixed Tensor, Tensor
Arfken, G. ``Noncartesian Tensors, Covariant Differentiation.'' §3.8 in
Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 158-164, 1985.
Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I.
New York: McGraw-Hill, pp. 44-46, 1953.
Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 44-46, 1953.
© 1996-9 Eric W. Weisstein