Diagrammatic Tensor Notation from the Beginning

In summary, the speaker has posted a link to a thread about Penrose's diagrammatic way of writing tensor algebra. They have spent time learning the basic notation but found it difficult due to limited information available. They plan to write a tutorial on how to use the notation for numerical computations and have 14 rough pages done. They are seeking suggestions for improving the tutorial and want to keep it short and simple.
  • #1
LukeD
355
3
I've posted this in the Geometry & Topology section, but I believe it will get many more views here, so I'm posting a link

Pictures here:
https://www.physicsforums.com/showthread.php?t=407776

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I really liked Penrose's diagrammatic way of writing tensor algebra, so I spent a while learning the basic notation. Unfortunately, it took a very long time for me to learn this because there is so little info on it to begin with. I also didn't see much mention of how to use the notation for doing numerical computations.

So since I want to be able to use the notation for everything that I should be able to do with tensors, I figured that I'd start at the very beginning of algebra and use the notation. My plan is to write a little tutorial that teaches everything from how to write numbers, vectors & covectors to how to take integrals.

The notation for adding tensors is mine as far as I know, and I've changed some other notation here and there.

I have 14 pages done, but they are very rough. So far they are very basic ideas. Should I continue with this? Any suggestions for cleaning it up? I want to make it as short & simple as possible while still getting the point across.
 
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  • #2
Can you teach me how to konw it
 

1. What is diagrammatic tensor notation?

Diagrammatic tensor notation is a mathematical notation system used to represent tensors, which are mathematical objects that describe the relationships between different vector spaces. It uses visual diagrams to represent tensor operations and their properties.

2. Why is diagrammatic tensor notation useful?

Diagrammatic tensor notation is useful because it allows for a more intuitive understanding of tensor operations. The visual diagrams help to visualize and understand the complex mathematical equations involved in tensor calculations.

3. How is diagrammatic tensor notation different from traditional tensor notation?

Diagrammatic tensor notation is different from traditional tensor notation in that it uses visual diagrams instead of mathematical symbols and equations. This makes it easier to understand and work with, especially for those who are more visually oriented.

4. Who uses diagrammatic tensor notation?

Diagrammatic tensor notation is primarily used by scientists and mathematicians in fields such as physics, engineering, and computer science. It is also becoming more popular in machine learning and artificial intelligence applications.

5. Are there any limitations to diagrammatic tensor notation?

While diagrammatic tensor notation is a useful tool, it does have some limitations. It may not be as efficient for complex calculations involving a large number of tensors, and it also may not be as widely used or recognized as traditional tensor notation in some fields.

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