Re: direct product and tensor product

On Jan 23, 2:26 pm, w...@xxxxxxxxxxxxxxxx (J. B. Wood) wrote:
In article <glckt3$1nn...@xxxxxxxxxxxxxxxxxx>, magi...@xxxxxxxxxxxxxxxxx

(Arturo Magidin) wrote:
Now, if you will get your panties untied for a second, you'll note
that I said that it was possible to talk about the uniquely determined
element of the tensor product of the vector spaces that "corresponds"
to particular vectors in the two spaces and the like.

Hello, and except for your underwear reference I don't have any idea what
the above is supposed to mean.  I consider myself an applied, rather than
abstract mathematician.  I think I have a decent understanding of vectors
and elementary tensor analysis.  I'll leave the manipulation of "vector
spaces" to others.  

This is simply meaningless ;-) You cannot manipulate vectors
and not vector spaces, for belonging to a vector space is what
turns an object into a vector.

-- m



.

Relevant Pages

  • Re: Vector space query
    ... Jacobson then goes on to give some motivation with mxn matrices continuing with a definiton of a tensor product using morphisms which is essentially the universal property. ... Look at Jacobson Lectures in Abstract Algebra Vol II, ... Then there is no mention of universality in Halmos' book of 1958 Finite-Dimensional Vector Spaces, but perhaps one should not expect that as the book is for FD spaces. ...
    (sci.math)
  • Re: direct product and tensor product
    ... I indeed looked more carefull into Lang book and found that he defines tensor product not on vector space MxN but on the set of bilinear maps from MxN into field K. This makes sence. ... Algebra by Lang. ...
    (sci.math)
  • Re: Vector space query
    ... with a definiton of a tensor product using morphisms which is essentially ... Look at Jacobson Lectures in Abstract Algebra Vol II, ... There is no mention of "universality" so presumably this concept was in its ... Finite-Dimensional Vector Spaces, but perhaps one should not expect that as ...
    (sci.math)
  • Re: Matrix notation (was Re: The Hodge dual...)
    ... > product of vector spaces. ... First let's do the tensor product of two vectors, ... of the row vector and the column ... The result will be a mp by nq matrix whose entries ...
    (sci.physics.research)