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tiny-tim
#2
Mar15-12, 06:48 AM
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hi lostminty!

(try using the X2 button just above the Reply box )
Quote Quote by lostminty View Post
[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]
fine
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
no, the whole point of knowing that ∂xi/∂xj = ejek = δij

is that this notation enables you to avoid using those "iffs"
ejekxjxk

= δjkxjxk

= xkxk
(and try the third one again)