0
$\begingroup$

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.

  • 0
    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.2012-04-15

1 Answers 1

2

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 $2$.