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I have the following equation and I am trying to simplify it:

$$\frac{\sum_{i=1}^M \sum_{j=1}^N [f(i,j) - h(i,j)]^2}{\sum_{i=1}^M \sum_{j=1}^N [f(i,j)]^2}=1-\frac{2\sum_{i=1}^M \sum_{j=1}^N f(i,j)h(j,j)+\sum_{i=1}^M \sum_{j=1}^N [h(i,j)]^2}{\sum_{i=1}^M \sum_{j=1}^N [f(i,j)]^2}$$

Is this simplification correct? If not what is the right answer?

Erik Kjellgren
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Sarmad
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  • I think you flipped a sign before $\sum_{i=1}^M\sum_{j=1}^N [h(i, j)]^2$. Otherwise, the equation is true, but in a pretty trivial way. I wouldn't really consider it "simplified." – Michael L. Aug 13 '17 at 20:26
  • You have a typo on the right side. $h(j,j)$ should be $h(i, j)$. – marty cohen Aug 13 '17 at 20:44

1 Answers1

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Hint:

Not exactly the same question but this can help you find your error.

$$\frac{\sum_{i}(a_i-b_i)^2}{\sum_ia_i^2}=\frac{\sum_i(a_i^2-2a_ib_i+b_i^2)}{\sum_ia_i^2}=1-\frac{2\sum_ia_ib_i-\sum_ib_i^2}{\sum_ia_i^2}$$

Siong Thye Goh
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