- #1
Elwin.Martin
- 207
- 0
B&F have the following:
[itex]\delta_{i j} = e'_i \cdot e'_j = a_{i k} \left( e_k \cdot e'_j \right) = a_{i k} a_{j k} [/itex]
and they ask the reader to show that
[itex] a_{k i} a_{k j} = \delta_{i j} [/itex]
Does it suffice to show the following? :
[itex] \delta_{i j} = a_{i k} a_{j k} \to \delta_{j i} = \left( a_{i k} a_{j k} \right)^T = a_{k i} a_{k j} [/itex]
and note that
[itex] \delta_{j i} = \delta_{i j} [/itex]
?
I believe this is sufficient, but I have a feeling I short-cut this.
[itex]\delta_{i j} = e'_i \cdot e'_j = a_{i k} \left( e_k \cdot e'_j \right) = a_{i k} a_{j k} [/itex]
and they ask the reader to show that
[itex] a_{k i} a_{k j} = \delta_{i j} [/itex]
Does it suffice to show the following? :
[itex] \delta_{i j} = a_{i k} a_{j k} \to \delta_{j i} = \left( a_{i k} a_{j k} \right)^T = a_{k i} a_{k j} [/itex]
and note that
[itex] \delta_{j i} = \delta_{i j} [/itex]
?
I believe this is sufficient, but I have a feeling I short-cut this.