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>
>
>
>

```

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