- #1

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I have an equation like this:

[itex]\sum_{i=0}^{n} x^{i}*y^{i}[/itex]

is there a way to re-express this equation by writing x and y separate? Thank you

- Thread starter femiadeyemi
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- #1

- 13

- 0

I have an equation like this:

[itex]\sum_{i=0}^{n} x^{i}*y^{i}[/itex]

is there a way to re-express this equation by writing x and y separate? Thank you

- #2

mathman

Science Advisor

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|x||y|cosθ, where θ is the angle between the vectors and |x| and |y| are the individual vector lengths. I suspect it won't be much help, since the usual way of finding the angle is using the dot product.

- #3

CompuChip

Science Advisor

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Assuming you want to rewrite your sum (and that * means scalar multiplication and not e.g. convolution) to something like

##\left( \sum f(x) \right) \left( \sum g(y) \right)##

where f(x) and g(y) are some functions of only the x's and y's, respectively, in general the answer is no - you cannot do that, except for what mathman has already pointed out.

However, I assume this question did not drop out of thin air; so maybe if you give us a bit more about the context that you asked it in we would be able to help you more.

- #4

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If you are trying to get estimates on something (like upper bounds) you can use Cauchy Schawrtz:

I have an equation like this:

[itex]\sum_{i=0}^{n} x^{i}*y^{i}[/itex]

is there a way to re-express this equation by writing x and y separate? Thank you

[itex]\sum_{i=0}^{n} x^{i}*y^{i} \leq (\sum_{i=0}^{n} x_i^2)^{1/2}(\sum_{i=0}^{n} y_i^2)^{1/2}[/itex]

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