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From: johnm@dbrmelb.dbrhi.oz (John Mashford)
Newsgroups: sci.math,sci.physics,comp.theory.dynamic-sys
Subject: tensors
Keywords: tensors, Minkowski space
Message-ID: <907@dbrmelb.dbrhi.oz>
Date: 31 May 91 07:56:26 GMT
Followup-To: poster
Organization: CSIRO, Div. Building Constr. and Eng'ing, Melb., Australia
Lines: 27

Hello networld,

I have the following problem with tensors:

Let eta = diag(1,-1,-1,-1) be the standard metric tensor for Minkowski space
and let < , > be the associated inner product.

By taking {e(i) : i = 0,...,3} to be the standard basis for Minkowski space we
can satisfy the following equations
    <e(i),e(j)> = eta(i,j), for i,j = 0,...,3.

My problem is to find 16 vectors {mu(i,j) : i,j = 0,...3} which satisfy
    <mu(i,r),mu(j,s)> = eta(i,j)eta(r,s).

If {mu(i,j)} is a solution and L is a Lorentz transformation then {L(mu(i,j))}
is also a solution.

Any help at all towards finding a solution or proving that no solution exists
would be very gratefully received.
___

| John Mashford   Commonwealth Scientific and Industrial Research Organization |
|                 Post Office Box 56, Highett, Victoria, Australia   3190      |
| Internet: johnm@mel.dbce.csiro.au  Tel: +61 3 556 2211  Fax: +61 3 556 2819  |
|______________________________________________________________________________|

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