What is the difference between lower division linear algebra and upper division linear algebra?
At my university, lower division LA is basically Matrix algebra and an intro to set theory and notation and that sort of stuff. I suppose the major difference where I attend is rigor and proof.
It depends on your school. Some schools have two linear algebra courses - one that focused on proofs and another that focused on applications. Other schools have a linear algebra sequence where the first class is spent on reducing matrices, finding eigenvalues, etc and the second course picks up at linear vector spaces.
At my school, the lower division class is basically matrix algebra. The upper division class is basically the same, except in the context of vector spaces and with all results proven. The upper division class is meant to be an introduction to proofs as well.
It is indeed very likely that lower division is just matrix algebra and upper division is vector spaces and stuff.
Perhaps you could post the course contents to be sure??
Solving linear systems, matrices, determinants, vector spaces, bases, linear transformations, eigenvectors, norms, inner products, decompositions, applications.
Introduces matrices, systems of linear equations, determinants, vector spaces, linear transformations, and eigenvalues.
Upper division is the same thing without the torture instruments. From my point of view, anyway. Actually, I have no idea, I'm just goofing off.
But the point is that if you just look at it from a matrix point of view without vector spaces, it's really awful stuff (if you're one of the people who likes to actually understand things). That was what my first linear algebra class was like, until we got to the end, but by then, it was too late. I didn't really learn linear algebra until I took analysis or maybe when I read visual complex analysis. Somewhere in there.
My schools LD linear is matrix algebra, inverses, determinants, vector spaces, inner product spaces, eigenvalue problems, least squares, spectral theorem and a couple other things I forget.
UD is still not proof oriented here but, at least when I took it, it was mostly on infinite dimensional vector spaces.
lower division (undergraduate) at where I went: matrix stuff, transformations, vector spaces, eigenvalues, determinants, systems of ODEs, intro to fourier, and complex vector spaces.
upper division (graduate) was: review of real/complex vector spaces and transformations, then isomorphisms, modules, metric spaces, hilbert spaces, and tensors. Abstract algebra was a prerequisite. Corequisite was either real or complex analysis.
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