Tensors

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Offline jeffreyH

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Tensors
« on: 20/03/2014 02:41:44 »
I am putting together a spreadsheet on tensors but at the moment I have no sensible values to feed into the formulas. Is there any information available for sensible values for these? I want to avoid complex numbers as I am just transforming values.

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Offline Pmb

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Re: Tensors
« Reply #1 on: 20/03/2014 02:58:36 »
I am putting together a spreadsheet on tensors but at the moment I have no sensible values to feed into the formulas. Is there any information available for sensible values for these? I want to avoid complex numbers as I am just transforming values.
That depends on what kind of tensor you have in mind and what it's physical meaning is.

Take a look at the Faraday tensor at http://home.comcast.net/~peter.m.brown/em/faraday_tensor.htm

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Offline JP

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Re: Tensors
« Reply #2 on: 20/03/2014 18:34:14 »
A tensor is basically a matrix and can be written as a collection of numbers.  Saying "what is a sensible value for my tensor" is like saying "I have a number, what's a sensible value for it?"  You need to give context, as Pete says.  It should have reasonable values for whatever physical meaning the tensor has. 

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Offline jeffreyH

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Re: Tensors
« Reply #3 on: 20/03/2014 23:57:24 »
I am putting together a spreadsheet on tensors but at the moment I have no sensible values to feed into the formulas. Is there any information available for sensible values for these? I want to avoid complex numbers as I am just transforming values.
That depends on what kind of tensor you have in mind and what it's physical meaning is.

Take a look at the Faraday tensor at http://home.comcast.net/~peter.m.brown/em/faraday_tensor.htm

Thanks Pete that is a good starting point.

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Offline jeffreyH

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Re: Tensors
« Reply #4 on: 21/03/2014 01:47:23 »
A tensor is basically a matrix and can be written as a collection of numbers.  Saying "what is a sensible value for my tensor" is like saying "I have a number, what's a sensible value for it?"  You need to give context, as Pete says.  It should have reasonable values for whatever physical meaning the tensor has.

Badly worded question.

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Offline Pmb

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Re: Tensors
« Reply #5 on: 21/03/2014 04:48:16 »
A tensor is basically a matrix and can be written as a collection of numbers.
That is incorrect. It gives the false impression that all matrices which are can be written as a collection of numbers is a tensor, which is not true. A tensor may be expressed in a particular coordinate system using matrices. A matrix represents a tensor if the components of the tensor transform in a special way when the coordinates are changed. As an example please see
Eq. (14) at http://home.comcast.net/~peter.m.brown/math_phy/tensors_via_analytic.htm

There are two ways to define a tensor (1) the analytic way and (2) the geometric way. See

http://home.comcast.net/~peter.m.brown/math_phy/tensors_via_analytic.htm
http://home.comcast.net/~peter.m.brown/math_phy/tensor_via_geometric.htm

Quote from: JP
Saying "what is a sensible value for my tensor" is like saying "I have a number, what's a sensible value for it?"  You need to give context, as Pete says.  It should have reasonable values for whatever physical meaning the tensor has. 
Good point. A good example of a very simple tensor is the proper mass of a particle. It's a single number, the mass of the particle in question. The charge of a particle is another example.
« Last Edit: 21/03/2014 04:52:33 by Pmb »