Vector analysis, comparing tensors to vectors

In summary, the conversation discusses the difficulty of understanding a homework question involving identifying a nontrivial second order tensor in R^2 with a first order tensor in R^4. The speaker is unsure about the concept and doesn't believe there is much information available on the topic.
  • #1
1MileCrash
1,342
41
I have been struggling with this homework question for a week and it still makes no sense to me.

I am asked to

"choose a nontrivial second order tensor in R^2 and determine whether or not it can be identified with a first order tensor in R^4 in a natural way, and if it can be, is every second order tensor in R^2 a first order tensor in R^4 in this natural way?"

What is he talking about? As far as I know they have the same number of components and that is it.
 
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  • #2
I don't think the entire internet has anything to say about this.

Swell.
 

Related to Vector analysis, comparing tensors to vectors

1. What is vector analysis?

Vector analysis is a mathematical tool used to study and manipulate vectors, which are quantities that have both magnitude and direction. It involves operations such as addition, subtraction, and multiplication of vectors, as well as the use of coordinate systems and vector components.

2. What are tensors?

Tensors are mathematical objects that can be used to represent and analyze physical phenomena that involve multiple directions and magnitudes. They are generalizations of vectors and matrices, and can have multiple dimensions and components.

3. How do tensors and vectors compare?

Tensors and vectors have some similarities, as they both involve direction and magnitude. However, tensors are more complex and can represent more complex phenomena, while vectors are simpler and can only represent one direction at a time. Tensors can also be used to generate vectors, but not vice versa.

4. What are some real-world applications of vector analysis and tensors?

Vector analysis and tensors are used in many fields, including physics, engineering, and computer science. They are used to study and analyze physical forces, such as in mechanics and electromagnetism, and are also used in computer graphics and image processing to manipulate and transform images.

5. Is vector analysis and tensors difficult to learn?

Like any mathematical subject, vector analysis and tensors can be challenging to learn. However, with a solid foundation in linear algebra and calculus, it is possible to understand and apply these concepts effectively. Practice and hands-on experience are also important for mastering vector analysis and tensors.

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