Linear Algebra and Calculus are different, and each is as hard as the course designer chooses to make it!
AoPS is accredited now, by the Western Association of Schools and Colleges, if that helps. Academically, the idea that one of its courses isn't as good as the corresponding course taken in a bricks and mortar school is laughable. I suppose it could be an issue that there's no invigilated final exam, but that seems to be common.
Point taken - The cohort/environment makes a huge difference. At my alma mater, Linear Algebra was treated more like an upper level course (less than two dozen Sophomores/Juniors majoring in Math/Applied Math) whereas Calculus was treated akin to a survey course because most of the Freshmen who did take it were repeating it.
I am not familiar with the Western Association of Schools but our district seems big on independently vetting everything. At one time, CTY was sometimes acceptable in certain limited circumstances as long as the student also jump through other independent hoops. For what it is worth, in addition to Alcumus, I really appreciate AOPS for providing curriculum such as Number Theroy, which are not routinely covered in schools. However, I do understand why our district would not accept online courses like AOPS by itself as a complete substitution. As a practical matter, the concept of an Honor System without oversight will never take root in our huge diverse system. There are also practical differences in curriculum and grading. In our district, writing/verbalizing math solutions is a huge component from 2nd grade onward and most of the grades come from unit tests and quarter exams which are always proctored.
I suppose this brings up the more general problem with many online courses where tests are not proctored and the teachers do not have regular spontaneous verbal interactions with students.
