hi lostminty!
(try using the X2 button just above the Reply box 
)
 Quote by lostminty
[itex]\frac{∂x_{i}}{∂x_{j}}[/itex] = 1 iff i=j
δ[itex]_{ij}[/itex] = 1 iff i=j
therefore
[itex]\frac{∂x_{i}}{∂x_{j}}[/itex] = δ[itex]_{ij}[/itex]
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fine
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r[itex]^{2}[/itex] = x[itex]_{k}[/itex]e[itex]_{k}[/itex][itex]\bullet[/itex]x[itex]_{j}[/itex]e[itex]_{j}[/itex]
= e[itex]_{k}[/itex]e[itex]_{j}[/itex]x[itex]_{k}[/itex]x[itex]_{j}[/itex]
e[itex]_{k}[/itex]e[itex]_{j}[/itex] = δ[itex]_{jk}[/itex] = 1 iff j=k
r[itex]^{2}[/itex] = x[itex]_{k}[/itex]x[itex]_{k}[/itex] iff j=k
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no, the whole point of knowing that ∂x
i/∂x
j = e
je
k = δ
ij
is that this notation enables you to
avoid using those "iffs" …
ejekxjxk
= δjkxjxk
= xkxk
(and try the third one again)