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What is meant by generic rank of a matrix? Is it something different from the rank, and does the word generic has just its English meaning? I came across this term in the book "Algebraic statistics for biology" (ed Lior Pachter and Bernd Sturmfels) theorem 19.5.

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Is there any particular reason why you're not quoting the sentence in which you encountered this expression? And you don't by any chance mean Algebraic Statistics for Computational Biology? Theorem 19.5 can be viewed at Google Books. – joriki Apr 15 '12 at 16:39
I didn't think the sentence would provide any additional information that would help anyone in answering the question ("The generic rank of the associated matrix is ..."). And yes, that's the book I am talking about. – Sangeeta Apr 15 '12 at 19:09
up vote 2 down vote accepted

I don't have the book, but I'll make a guess: I suspect the matrix in question depends on one or more parameters, and the author means that for "generic" values of those parameters the matrix has a certain rank. In this context "generic" can mean "in a dense $G_\delta$ set". For example, the matrix $$\pmatrix{p & 0\cr 0 & q\cr}$$ has rank $2$ unless $p=0$ or $q=0$, so you might say it has generic rank $2$.

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