What is the annihilator of a tensor in vector space V?

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In summary, The problem is to find the annihilator of a given tensor in a specific vector space. The answer can be found on Stack Exchange, but it may be difficult to understand for someone with limited knowledge of tensor algebra.
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Sudharaka
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Hi everyone, :)

This is a question I don't understand at all. What is the annihilator in this context? Hope you can help me out with this.

Problem: Find the annihilator of the tensor \(e_1\wedge e_2+e_3\wedge e_4\) in \(V=\left<e_1,\,e_2,\,e_3,\,e_4\right>\).
 
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  • #2
Sudharaka said:
Hi everyone, :)

This is a question I don't understand at all. What is the annihilator in this context? Hope you can help me out with this.

Problem: Find the annihilator of the tensor \(e_1\wedge e_2+e_3\wedge e_4\) in \(V=\left<e_1,\,e_2,\,e_3,\,e_4\right>\).

Hi everyone, :)

I have received an answer to this question on Stack Exchange. I am trying to understand it but due to my limited knowledge of tensor algebra it will take a long time. :p

linear algebra - Annihilator of a Tensor - Mathematics Stack Exchange
 

What is the "Annihilator of a Tensor"?

The annihilator of a tensor is a mathematical operation that transforms a tensor into a vector. It is also known as the contravariant dual of a tensor. It is denoted by a superscript asterisk (*).

How is the annihilator of a tensor calculated?

The annihilator of a tensor is calculated by taking the transpose of the tensor and then multiplying it by the inverse of the metric tensor. This results in a vector that is orthogonal to the original tensor.

What is the significance of the annihilator of a tensor?

The annihilator of a tensor is important in mathematical and physical applications. It allows for the transformation of a tensor into a more manageable vector, making it easier to perform calculations and analyze data.

What are some real-world applications of the annihilator of a tensor?

The annihilator of a tensor has various applications in fields such as physics, engineering, and computer graphics. For example, in physics, it is used to study the stress and strain on materials, while in computer graphics, it is used for image processing and pattern recognition.

Are there any limitations to the use of the annihilator of a tensor?

While the annihilator of a tensor is a useful mathematical tool, it has some limitations. It can only be applied to tensors with a specific number of indices, and it does not work for all types of tensors. It also requires a metric tensor, which may not always be available in certain applications.

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