For an arbitrary basis

(i) The duality relation (24.8),

(ii) The definition (24.9) of components of a tensor,

(iii) The relation

between the metric and the inner product to deduce the following results.
(a) The relations

(b) The fact that indices on the components of tensors can be raised and lowered using the components of the metric:

(c) The fact that a tensor can be reconstructed from its components in the manner of Eq. (24.11).

Transcribed Image Text:

{e} and its dual basis {e"},