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I am following the text by Isaacs on character theory and I have a few questions.

From p. 10, it seems like an reducible representation is one whose matrix at each group element can be written in a block diagonal form. However, the proposition on p. 20 states that the matrix of a representation at every group element can be written as a diagonal matrix. This would imply that every representation is reducible, which is clearly nonsense. What am I missing here?

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    I think it would be better to post these as two separate questions, as they're not related. Then searches can be more specific, and it's easier to keep track of the answers and how they relate to each other etc.2011-04-13
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    (Three questions)2011-04-13

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