Question: 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

For an arbitrary basis

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

(i) The duality relation (24.8),

image

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

image

(iii) The relation

image

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

image

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

image

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

image

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

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