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  4. Can a tensor be represented as a group of “connected” vectors?
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Can a tensor be represented as a group of “connected” vectors?

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Offline Richard777 (OP)

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Can a tensor be represented as a group of “connected” vectors?
« on: 17/08/2019 01:37:50 »
Can vectors be connected to form a vector structure?
Does this structure represent a tensor?
This tensor would have two (or more) magnitudes.
Two vectors may be assumed to be “connected” if;
   - they share a common origin (tail)
   - they share a common component.
Is this a useful representation of a tensor?
* Reference.pdf (193.54 kB - downloaded 49 times.)
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Offline yor_on

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Re: Can a tensor be represented as a group of “connected” vectors?
« Reply #1 on: 17/08/2019 16:24:44 »
Richard, where do you get out from?
A global representation or a local?
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Re: Can a tensor be represented as a group of “connected” vectors?
« Reply #2 on: 17/08/2019 23:01:43 »
The path to your PDF is so convoluted that, by the time I got to it, I just couldn't even be bothered to read it.
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Re: Can a tensor be represented as a group of “connected” vectors?
« Reply #3 on: 18/08/2019 16:06:26 »
Quote from: Richard777 on 17/08/2019 01:37:50
Can vectors be connected to form a vector structure?
Without seeing an example it is difficult to understand what you mean.
However, by your definition of connected:
Quote from: Richard777 on 17/08/2019 01:37:50
Two vectors may be assumed to be “connected” if;
   - they share a common origin (tail)
   - they share a common component.
If two vectors are arranged in this way, assuming that both magnitudes have the same denomination, then you will have a resultant vector.

Quote from: Richard777 on 17/08/2019 01:37:50
Does this structure represent a tensor?
As all vectors are tensors, then if the resultant is a vector then yes.

Quote from: Richard777 on 17/08/2019 01:37:50
This tensor would have two (or more) magnitudes.
Then it’s not a tensor - unless you mean components of the tensor. Give an example - don’t just link to an external website, that is not discussing a topic on this website (see our usage policy).

Quote from: Richard777 on 17/08/2019 01:37:50
Is this a useful representation of a tensor?
Doesn’t sound like it.
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