In a subsection titled "Defective Eigenvalues and Matrices" the opening paragraph reads
Although a generic matrix has algebraic and geometric multiplicities that are equal (namely, all 1), this is by no means true of every matrix.
Maybe it's just me not being used to the jargon, but I take generic to mean any matrix, in general; but then the author's statement is obviously false. I think this must be an incorrect intpretation (by me). So what's going here? Is generic a specialized term?
I've seen no definition of generic in the text so far.
This is a specialized use of generic in mathematics. Informally, a property is generic if it holds for most cases, or except on a set of measure 0, or something similar to that. See the Wikipedia discussion of this.