Talk:Dual space
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This is fine math, but no one has even defined a basis for a Vector Space, given the standard geometric interpretation of R3 as a Vector Space (a good concrete example.), etc. Lets try to fill in the more elementary material, before we soar to these heights...:-). I guess that includes me, too. RoseParks
I moved Rose's comment here, partly because there is at least entry for basis of a vector space now. DMD
I've seen what you call the "continuous dual" denoted by X* as well. Often the distinction is entirely based on context, if you're just working with vector spaces, X* is the algebraic dual, if you're workign with normed spaces, it's the continuous one. It might be worth noting this, because I for one have been confused by texts working with what they call X* when they mean what you call X'. cfp 22:37, 4 Apr 2004 (UTC)
I read elsewhere that a square matrix can be thought of as a tensor with one covariant index and one contravariant index. So it seems to me that row and column vectors correspond to tensors like <math>A^i, B_j<math>. If dual spaces have to do with the relation between row and column vectors, does it have something to do with tensors?
- Well, yes. General tensors on a vector space V are built up from the tensor product of some copies of V and its dual space. Charles Matthews 09:56, 11 May 2004 (UTC)