Talk:Bilinear map

Untitled
Whoever put this in:

"In other words, if we hold the first entry the bilinear operator fixed, while letting the second entry vary, the result is a linear operator, and similarly if we hold the second entry fixed."

thankyou!

How about another example for a matrix $$B\in M_n(F)$$ as a bi-linear form: $$B : F^nxF^n->F$$ defined by $$v^TBw$$, $$v,w\in F^n$$

map vs operator
I think the term "operator" should be reserved for maps of a space into itself (or by extension ExE&rarr;E), while for the general case (in particular bilin.forms) the term "map" should be preferred. &mdash; MFH: Talk 17:46, 27 May 2005 (UTC)


 * Agree. At any rate, we should keep our naming consistent; witness multilinear map vs. bilinear operator. -- Fropuff 18:03, 2005 May 27 (UTC)


 * Seems reasonable. I was wondering about the same topic some time ago. This should be put at WikiProject Mathematics/Conventions.MathMartin 11:03, 29 May 2005 (UTC)


 * I've partially fixed this, but haven't gone so far as to move the page: I would, however, support such a move. Geometry guy 16:35, 13 May 2007 (UTC)


 * Yes, I agree. Someone with operator privs should perform the move. --MarSch 17:47, 13 May 2007 (UTC)

Pairing
How is this article related to pairing? It seems there is an overlap. Nageh (talk) 16:22, 26 May 2010 (UTC)


 * I think the question should be: Shouldn't this article be extended to cover modules? Meaning, we get R-bilinear maps, which should probably be covered in this article, and then pairing (which is evidently just an R-bilinear map) should be a redirect here. K-bilinear maps (K being a field, so this is what is currently covered by this article) are merely special cases of R-bilinear maps, which is the subject of Pairing. — Quondum 16:31, 9 September 2012 (UTC)

Inverse of bilinear map
For the case, VxV->F, I guess the inverse of the bilinear map should be well defined because the map is commutative, if $$f(a,b)=c$$, then $$f^{-1}(c,a)=b$$ and $$f^{-1}(c,b)=a$$. Is this right? and is it meaningful? is it well defined? Jackzhp (talk) 05:54, 8 May 2015 (UTC)
 * The appropriate place to ask this would be at WP:RD/MA. —Quondum 13:02, 8 May 2015 (UTC)

Diagram Needed
It would be much easier to understand this article if there were diagrams that showed the process. The information provided is merely textual and gives the reader a difficult time understanding the underlying principles. Senomo Drines (talk) 15:04, 31 October 2022 (UTC)