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Comment by sopooneo | Hacker News Reader

Here's one I think is probably 101 level for others here, but what is the difference between a multidimensional scalar and a vector? I'll gratefully read through any reference you can link to.

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Whether something is 101-level or a difficult thesis topic often depends on your point of view. Different fields seem to define scalars differently, with the physicists sometimes arguing that the mathematicians have got it all wrong: http://imechanica.org/node/15857

On a related note, I was tremendously impressed with the quality of discussion at imechanica.org. At a glance, it may be the best example of a well-functioning online community that I've ever seen.

It looks like he's fumbling towards replacing the field with a (graded?) ring and therefore replacing vector spaces with modules.

Great part: "They should not call the elements in the number field F scalars. These elements already have names: they are called numbers. And we physicists and engineers need the word scalar to name some other objects. Mathematicians, like physicians, should at least learn to do no harm. "

A vector belongs to a vector space, which implies certain algebraic rules relating it to other vectors in the space (http://en.wikipedia.org/wiki/Vector_space is probably enough reference). A multidimensional scalar is a more general data type, as any or all of the vector axioms can be relaxed or eliminated.

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