# What does the following symbol mean? (direct sum? o-plus? — subject: matrix theory)

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. – Mlazhinka Shung Gronzalez LeWy 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

"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).
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