ComicBookDude said:

I meant 6 classes (Real Anal 1+2, Abstract Algebra 1+2, 2 upper level electives and maybe an intro to comp programming)

no mathematical history class?

j/k.

anyway, if you took linear class using decent text such as hoffman and kuntz or axler and did well in that class, you probably will not have alot of problems with the intro. analysis. but if you took linear with sparse proofs or brute(calculation heavy) force proofs, you might suffer due to lack of familiarity with the higher math text format/proof.

typically undergrad. offers two linear courses; a service course and the actual math major-intended linear algebra. it's like intro physics course where there are algebra based and calc. based one.

if you took the "service course" you might not have experienced enough proofs and will need to take other proof heavy courses such as abstract, number theory, topology, etc, before venturing into analysis course.

in my personal opinion, one of the best way to test whether you might be ready for a course or not, is buying the text and read it and see whether you can follow the material clearly. if you could do that for at least 4 or 5 chapters(approx. 1/4 to 1/3 of the whole text), you are good to go.