Talk:Dual basis

As said in Requested articles/Linear algebra:

"Searching for "dual basis" directs to the article Dual basis in a field extension which is not helpful for someone who is trying to grasp the idea of a dual basis."

So I've stopped it from redirecting...I can't write the article tho; someone else who knows about it will have to...Scholarus 00:41, 15 December 2006 (UTC)

Orthogonality?

To quote the main aritcle:

In linear algebra, a dual basis is a set of orthogonal vectors that span (i.e., they form a basis for) the dual space of a vector space.

Is the condition of orthogonality unecessary? Frigoris 20:36, 1 July 2007 (UTC)

Orthogonality is not a necessary condition. 165.91.14.55 (talk) 21:41, 23 February 2010 (UTC)

Needs expansion

Dual basis a are better understood with non orthogonal examples... how do you write the equations? I'd help improve this but need to know if WP has some tools to help editing equations? — Preceding unsigned comment added by 87.4.237.43 (talk) 18:36, 6 January 2013 (UTC)

Transpose of a vector

I removed the extrapolation of the transpose of a coordinate vector to coordinate-free vectors from the article. It was even presented as a primary motivation for the dual space, but since this extrapolation only works for a strictly orthonormal basis (implying in turn the structure of a positive-definite quadratic form) and is thus not basis-free (coordinate-free) and is most certainly not natural, this is fundamentally misguided. A dual basis, on the other hand, finds application in vector spaces without a defined quadratic form or indeed with any quadratic form, and we must conclude that its motivation came from something other than the transpose of vectors. — Quondum 02:10, 5 June 2013 (UTC)