- #1
izzi wekwek
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Asymmetric Tensor: Overview & Uses
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- Thread starter izzi wekwek
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In summary, the conversation discusses proper formatting for homework problems and the use of LaTeX for equations. It is recommended to use the homework template and the PF LaTeX feature for equations. The concept of antisymmetry and its simplification in summation is also mentioned. The individual's question about calculating a term is answered with the suggestion to clarify what is being asked for.
- #2
PeterDonis
Mentor
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Is this a homework problem? If so, it should go in the appropriate homework forum, and the homework template should be filled out.
Also, formulas should not be pasted in as images; they should be done using the PF LaTeX feature. Otherwise it's impossible for people to quote your formulas properly when responding.
Also, formulas should not be pasted in as images; they should be done using the PF LaTeX feature. Otherwise it's impossible for people to quote your formulas properly when responding.
- #3
izzi wekwek
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No, this is not a homework, I just learn by myself. thank you for your suggestion.
- #4
jtbell
Staff Emeritus
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If you generated your equations using LaTeX, simply enclose the code for each equation between $$ delimiters on each side (for standalone equations) or ## delimiters (for "inline" equations, embedded inside a paragraph).
- #5
haushofer
Science Advisor
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We also don't know how to calculate the term, because you don't give us what this omega is. Because omega is antisymmetric, the summation however simplifies, because only ##\frac{1}{2}D(D-1)## components of it are independent.
- #6
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To answer the original question, you have to tell us what you want to achieve. I don't understand what you mean by "how to calculate it". It's just the expression you wrote down, what else should it be?
What is an asymmetric tensor?
An asymmetric tensor is a mathematical object that represents the relationship between two vectors in space. It has both magnitude and direction, but unlike symmetric tensors, its components are not equal in all directions.
How is an asymmetric tensor different from a symmetric tensor?
An asymmetric tensor differs from a symmetric tensor in that its components are not equal in all directions. This means that the tensor is not invariant under rotation, and its behavior can vary depending on the coordinate system used to describe it.
What are some common uses of asymmetric tensors?
Asymmetric tensors have many applications in physics and engineering. They are commonly used to describe the stress and strain in materials, as well as the motion and deformation of objects. They also play a crucial role in fluid dynamics and electromagnetism.
How are asymmetric tensors represented mathematically?
Asymmetric tensors are typically represented using index notation, where each component is denoted by a subscript or superscript. The number of subscripts or superscripts corresponds to the dimensionality of the tensor, and the values of the indices indicate how the tensor transforms under a change of coordinates.
Are there any real-life examples of asymmetric tensors?
Yes, there are many real-life examples of asymmetric tensors. Some common examples include the stress and strain tensors in materials, the polarizability tensor in electromagnetism, and the gradient tensor in vector calculus. Asymmetric tensors can also be found in everyday objects such as bridges, airplanes, and car parts.
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