Re: Re: TensorQ
- To: mathgroup at smc.vnet.net
- Subject: [mg20800] Re: [mg20767] Re: TensorQ
- From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
- Date: Sun, 14 Nov 1999 18:13:50 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
I am afraid that high school is not enough here. Tensors are multilinear functions on the cartesian product of copies of a finite dimensional vector space and its conjugate. By choosing a basis for the vector space they can be made to correspond to vectors, matrices, and their higher rank generalizations (like matrices of vectors etc). Taking your example: an inner product corresponds to a positive-definite symmetric bilinear matrix (or a quadratic form). So there is nothing wrong with Ted's notion of a tensor. -- Andrzej Kozlowski Toyama International University Toyama, Japan http://sigma.tuins.ac.jp/ > From: "Yukio Hamada" <y-hamada at pop12.odn.ne.jp> > Organization: odn.ne.jp > Date: Thu, 11 Nov 1999 00:22:44 -0500 > To: mathgroup at smc.vnet.net > Subject: [mg20800] [mg20767] Re: TensorQ > > How do you do. > > Sorry . my Engilish composition is broken. > I am studying it now. > >> I was thinking it would be nice to have a function that determines if >> something is a vector, matrix, or higher dimension analogue of a matrix. > Is >> something like that called a tensor? I know almost nothing about tensors. > > > I think Your notion is mistake. (Excuse me) > Tensor is a mapping from a Vector space (V(*V)) to a real number (R). > > Tensor : V*(*V) -> R > > For Example , there is the Inner Product (a,b). Here "a" and "b" are > elements of V. > > (a,b) = cos*|a|*|b|. (This ia a real number) (V*V -> R). > > Did you learn at High School ?. > > Referrences > "Applied Differential Geometry" William L. Burke Cambridge UP. > > For your useful. > > PS: > I connat understand MASMATICA. > > << Yukio Hamada <y-hamada at pop12.odn.ne.jp> > > >