Talk:Linear form/Archive 1

Archive 1

Kernel

The page mentiones "kernel" but doesn't define it. —Ben FrantzDale 03:45, 1 December 2006 (UTC)

One-Form

Not a good idea to merge in the article on one-form because the one-form has a special use in relativity —The preceding unsigned comment was added by 81.86.127.58 (talk) 23:19, 14 March 2007 (UTC).

I disagree. This issue is currently being addressed at Talk: One-form; see the discussion there. Komponisto 00:32, 26 March 2007 (UTC)

Dual space

The notion of dual space is already discussed in great detail in the article Dual space. The purpose of this article is not to list the various properties of dual spaces. In particular, the assertion that the dual space has the same dimension as V is not true in general (only if V has finite dimension). In fact, the algebraic dual space of an infinite-dimensional vector space never has the same dimension as V. So I would prefer to leave the discussion of the dual space to the dedicated article on the subject. siℓℓy rabbit (talk) 19:03, 7 December 2008 (UTC)

I relied on http://mathworld.wolfram.com/DualVectorSpace.html. Whoever wrote the original dual space material probably meant n-vector, with reference to the case where V is Rn. I'll take your word for it re infinite-dimensional spaces being an exception, and that "the same dimension" would not be understood as both infinite.

I have no objection to saying less about dual-spaces on this page. My edit was to return the intro to the scope it had when I raised the issue of the dual space being a "k-vector space", but with improved clarity. You could remove "is a vector space over the field k" to be consistent.Paul V. Keller (talk) 21:46, 7 December 2008 (UTC)

Why would I remove the latter statement? The sentence is intended to convey that the set of all linear functionals on a vector space is <dramatic pause> a vector space and that this vector space is called the dual space. I am assuming that somehow this is not as clear as it should be? siℓℓy rabbit (talk) 22:18, 7 December 2008 (UTC)

"vetor space over the field k" is giving a property of the dual space, which your protested earlier was to no purpose given that there is a whole page on dual spaces. If you think it is inappropriate to mention the similarity of the dual space to the space V in the finite dimensional case to help give a sense of what a space of linear functions on Rn or any other space might look like, if you cannot see how mentioning something like that might be useful to someone seeing the dual space and linear functional definitions for the first time, you might as well just define the dual space and leave it at that, or not even define the dual space at all in the intro.Paul V. Keller (talk) 23:05, 7 December 2008 (UTC)

Strictly speaking, the article does just define dual spaces. The vector space structure they support is part of their definition. You seem to be insisting that we should think of the dual space not as a vector space but as a set? siℓℓy rabbit (talk) 23:28, 7 December 2008 (UTC)