If V is an odd-dimensional real vector space, then is there a linear map $J: V \to V$ satisfying $J^2=-1$? i.e. is there a complex structure in odd-dimensional real vector space?
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I guess you mean odd-dimensional Real vector space? – user99680 Apr 26 '14 at 07:35
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Of course. @user99680 – Yui Apr 26 '14 at 07:37
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Yes, sorry to ask, but we get all sorts of questions in here. – user99680 Apr 26 '14 at 16:39
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What would the determinant of such a J be?
Mariano Suárez-Álvarez
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This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. – naslundx Apr 26 '14 at 08:08
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@naslundx, the content of what I wrote is exactly the same as that provided by the accepted answer (and was posted before it). You will notice that I was neither critiquing not requesting clarification, but asking a question, answering which would have resulted in the OP solving his problem. – Mariano Suárez-Álvarez Apr 26 '14 at 08:18
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You are correct, I saw your answer in the review queue (someone else flagged it first) and might have misjudged. Either way, I would suggest starting such a question-answer with the common "Hint:"-text. – naslundx Apr 26 '14 at 09:22
