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DeShark
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Homework Statement
Write out [itex]c_{j}x_{j}+c_{k}y_{k}[/itex] in full, for n=4.
Homework Equations
The Attempt at a Solution
So I figure we have to sum over both j and k. So the answer I obtained is:
[itex](c_1x_1+c_1y_1)+(c_1x_1+c_2y_2)+(c_1x_1+c_3y_3)+(c_1x_1+c_4y_4)+[/itex]
[itex](c_2x_2+c_1y_1)+(c_2x_2+c_2y_2)+(c_2x_2+c_3y_3)+(c_2x_2+c_4y_4)+[/itex]
[itex](c_3x_3+c_1y_1)+(c_3x_3+c_2y_2)+(c_3x_3+c_3y_3)+(c_3x_3+c_4y_4)+[/itex]
[itex](c_4x_4+c_1y_1)+(c_4x_4+c_2y_2)+(c_4x_4+c_3y_3)+(c_4x_4+c_4y_4)[/itex]
i.e. [itex]4(c_1x_1+c_2x_2+c_3x_3+c_4x_4+c_1y_1+c_2y_2+c_3y_3+c_4y_4)[/itex]
but the book I'm working from just gives the answer:
[itex]c_1x_1+c_2x_2+c_3x_3+c_4x_4+c_1y_1+c_2y_2+c_3y_3+c_4y_4[/itex]
so I'm a factor of 4 out. Am I doing it wrong or is the book.
Surely the answer the book gave can be written
[itex]c_ix_i+c_iy_i[/itex]
Apologies for the noobiness of the question, but I'm trying to self-teach tensor calculus and I want to nail the basics before I progress much further.