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In this paper equation 11, the author uses a symbol that is a cross in a circle. I believe I have seen that referred to as a direct sum, but I am not completely sure what that is.

$$\bigoplus$$

This one

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Yes, they are putting one of those exponentials in each entry of the diagonal. That is like taking the map that in the direct sum acts by multiplying by the corresponding exponential. –  ABC Jul 17 '13 at 18:34
    
@DouglasS.Stones You should make that an answer. –  Pedro Tamaroff Jul 17 '13 at 18:37
    
Okay, I did that. –  Douglas S. Stones Jul 17 '13 at 18:43
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1 Answer

up vote 1 down vote accepted

This is an example of, what I call, a two-pass paragraph (I try to avoid these when writing). It's a situation in which you need to keep reading to understand the previous material.

If you keep reading, you'll find:

"In Eq. (11) the symbol $\oplus$ means matrix direct sum."

So $\phi(y)$ is the $4 \times 4$ diagonal matrix with the diagonal entries as listed in (11).

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Thanks. I was getting really confused because I thought he was saying that $\phi(y)$ was the W matrix. Wasn't sure what a direct sum was either so thanks! –  yankeefan11 Jul 17 '13 at 18:44
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