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March 29, 2024, 12:10:06 pm

Author Topic: Wtf are tensors  (Read 5701 times)  Share 

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Wtf are tensors
« on: May 17, 2011, 09:16:36 pm »
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From the lecture notes:

Write the following operations in terms of vectors and matrices:
, , , ,

Can someone show me how to interpret these... thanks

TrueTears

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Re: Wtf are tensors
« Reply #1 on: May 17, 2011, 09:32:43 pm »
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lol, sorry but this just totally reminds me of tensor tenergy table tennis rubbers LOL, one of the best rubbers around nowadays, probably the physics behind them makes em so pr0pr0pr0
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Re: Wtf are tensors
« Reply #2 on: May 17, 2011, 09:48:31 pm »
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lol, sorry but this just totally reminds me of tensor tenergy table tennis rubbers LOL, one of the best rubbers around nowadays, probably the physics behind them makes em so pr0pr0pr0

LOL xD
As exams get nearer i get tensor and tensor everyday

TrueTears

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Re: Wtf are tensors
« Reply #3 on: May 17, 2011, 10:52:41 pm »
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lol, sorry but this just totally reminds me of tensor tenergy table tennis rubbers LOL, one of the best rubbers around nowadays, probably the physics behind them makes em so pr0pr0pr0

LOL xD
As exams get nearer i get tensor and tensor everyday
LOL same here, gl on ur exams btw :D ull own them like always
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jimmy999

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Re: Wtf are tensors
« Reply #4 on: May 18, 2011, 07:58:30 pm »
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Go to here http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/documents/Tensors_TM2002211716.pdf

Lovely little read about them. I can't wait to learn them next semester :)
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mark_alec

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Re: Wtf are tensors
« Reply #5 on: May 18, 2011, 09:47:17 pm »
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I'll assume in all cases that the indices go over the values 0,1,2,3 (Lorentz indices, for relativistic things).

When you have the same index, one upstairs, one downstairs, the lingo is that you "contract" the objects, which is a fancy way of saying do something like a Minkowski inner product.

For example:
, a scalar. The second one has two different indices, so you don't contract them together. The object it represents will be like the outer product of the two 4-vectors (rather than the inner product if they have the same index).

You can think of indices as generalisations of scalars, vectors, matrices - the rank corresponds to the dimensions (0, 1 and 2 respectively).
« Last Edit: May 18, 2011, 09:48:53 pm by mark_alec »

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Re: Wtf are tensors
« Reply #6 on: June 02, 2011, 04:51:45 am »
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For example:
, a scalar.
That's only for Minkowski space using the signature (+,-,-,-) right?

That is one application of the Einstein notation for tensors (or Einstein summation notation). Tensors are just matrices with higher orders (i.e. 3rd order tensor requires two index to pin-point an element, etc. Vectors are 1st order tensors, matrices are 2nd order tensors.) For the Einstein notation, if an index appears twice in one term, it represents a sum over the degrees of freedom (dimensions) of the tensor, e.g.

where n is the degree of freedom

Not quite sure how to interpret the latter few of your expressions, what is the order of a and b? (matrices? 3rd order tensors?)
« Last Edit: June 02, 2011, 04:55:03 am by Mao »
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QuantumJG

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Re: Wtf are tensors
« Reply #7 on: June 22, 2011, 10:40:55 pm »
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Tensors are just awesome things to use. Especially in relativity if you want to measure the current density in a loop moving at a relativistic speed, etc.
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