Mathview's video: Intro to the Metric Tensor Part 2 wmv

In a previous video we examined the metric tensor as a bilinear functional mapping pairs of vectors to the real numbers. In Part 2 we examine the metric tensor as a bijective mapping between vectors and functionals. We derive the "raising and lowering" property of the matrix g and its inverse. We introduce the rank of a tensor and the tensor type notation (p,q). Tensors of the same type form a linear space. This allows us to represent tensors in terms of basis tensors composed of tensor products of basis vectors in Vn and Vn*. Hence we can prove that the bilinear functional G(x,y) is equal to a tensor of second rank.