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I read this sentence in a report concerning in symmetric cone programs: "Let J be a Euclidean Jordan algebra with dimension n, and rank r." I know what the rank of a (matrix) is.. does the rank here have the same meaning for a vector space, "the maximum number of linearly independent vectors" ? Thank you in advance.

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The definition of "rank" for a Euclidean Jordan algebra is as follows, see here:

Definition: The maximal number of elements in a Jordan frame is called the rank. (Jordan frame has to do with idempotents).

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