Talk:Sublinear function

Positive homogenity

I do not get the rule about positive homogenity. Does this mean for example $log(\cdot )$ , where $\log(\gamma x)=\log(\gamma )+\log(x)$ , is not a sublinear function? This is a bit different from what sublinearity means when using Big O notation. -- Nils Grimsmo 06:05, 27 June 2006 (UTC)[reply]

Beyond convex or concave class

Doesn't a sublinear function exist beyond convex or concave class? (Moved question by 149.135.14.246 at 2007-03-05T17:26:48 from article to talk page) Nils Grimsmo 20:33, 6 March 2007 (UTC)[reply]

Asymptotic analysis

I've changed the wording about the variable "c" according to Big_O_notation. Instead of being able to use just any value for c, there should be at least one possible value (hence the existential quantifier in the Big O article). --Andreasvc (talk) 14:29, 24 June 2008 (UTC)[reply]

Now I get it, it should be "any given c" because this is what makes it different from linear functions...--Andreasvc (talk) 14:32, 24 June 2008 (UTC)

Sublinear vs. Semi-norm

So sublinear functions from a vector space to the reals are semi-norms? Maybe we should note that in properties. —Preceding unsigned comment added by 141.254.25.140 (talk) 14:45, 16 July 2008 (UTC)[reply]

No they are not the same : a semi-norm p must also verify p(-x)=p(x), which is not required for a sublinear function. French Tourist (talk) 17:46, 16 July 2008 (UTC)[reply]

But -x = (-1)x, so can't we just apply homogeneity? And we know that -1 is in the field, since that has a multiplicative identity and additive inverses... 141.254.25.140 (talk) 14:51, 17 July 2008 (UTC)[reply]

The functionals are assumed to be only positive homogeneous, not homogeneous. So your argument does not apply. Delio.mugnolo (talk) 14:14, 1 July 2013 (UTC)[reply]

Mismatched definitions

I think that the $o(.)$ definition is out of place here. The rest of the article describes properties of the linear algebra concept, without specifying which meaning is used. The two concepts are very different and should have different articles, despite having the same name. Does anyone agree? LachlanA (talk) 09:25, 24 April 2010 (UTC)[reply]

I agree that the o(.) definition is a bit out of place. Also note that there exist redirects from sublinear time and sub-linear time to time complexity#Sub-linear time. It might be enough to replace the o(.) definition with a hatnote. —Tobias Bergemann (talk) 13:01, 12 May 2010 (UTC)[reply]

$X$ as vector space over $\mathbb {R}$

Of course $X$ can be supposed to be a vector space over $\mathbb {R}$ , because there is no complex scalar multiplication involved in the definition! 129.104.241.162 (talk) 02:46, 11 March 2024 (UTC)[reply]

Field of Scalars

Over on Talk:Seminorm, the question is posed: Is there any reason we restrict to vector spaces over R or C? The definition makes sense for vectors spaces over any valued field, right? This question applies equally here, as well. (I think the answer is "yes", so the real question is "how do we deal with this?") 67.198.37.16 (talk) 20:02, 27 May 2024 (UTC)[reply]