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Re: Re: TensorQ

  • To: mathgroup at
  • Subject: [mg20800] Re: [mg20767] Re: TensorQ
  • From: Andrzej Kozlowski <andrzej at>
  • Date: Sun, 14 Nov 1999 18:13:50 -0500 (EST)
  • Sender: owner-wri-mathgroup at

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
Andrzej Kozlowski
Toyama International University
Toyama, Japan

> From: "Yukio Hamada" <y-hamada at>
> Organization:
> Date: Thu, 11 Nov 1999 00:22:44 -0500
> To: mathgroup at
> 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>

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