Anonymous wrote: > > Marc: > > >The first time, I spent in a linear algebra course (Kaiserslautern, 1986) > >introduced sets, groups, rings and fields, modules and then vector spaces. > >(in that order) > > Odd. We did sets and then groups in algebraic structures. We touched upon > rings, I think, but I don't remember what they are. Have no idea about fields,
The definition of vector space will mention scalars. The scalars form a field.
> if they're not vector fields, which someone already said they aren't. Never > heard of modules. > > We did vectors, then vector spaces, then subspaces. Then spans, dependence, > bases, matrices, determinants, then eigenvalues and vectors. It's odd because > Schaum's Outlines does it in a different order. And Cliff's does an even > different order. > > >By the time we met vector spaces, the notion of image and kernel as well > >as the proof of the first homomorphism theorem > > "Homomorphism theorem"? Is this what's called "Dimension Theorem" now?
> > >But nowadays nobody needs to be afraid of modules in a linear algebra course, > >unless it is only a MMC (Matrix Manipulation Course). > > > > What are modules? And why are they related to marix manipulation? BTW, I, for
In the definition of vector space, replace "field of scalars" with "ring".
> one, would love to have taken a linear algebra course that was all MMC. I love
An MMC wouldn't be a linear algebra course. There are vector spaces that have nothing to do with matrices.
> the stuff!
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