Asymmetric Tensor: Definition & Examples

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Thread starter izzi wekwek
Start date Mar 13, 2016
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In summary, an asymmetric tensor is a mathematical object used to represent multilinear mappings between vector spaces that is not symmetric under interchange of its indices. This means that switching the order of its arguments can result in a different value. It differs from a symmetric tensor, which remains unchanged when its indices are interchanged. Examples of asymmetric tensors include the stress tensor, electromagnetic field tensor, and Riemann curvature tensor. These tensors have various applications in physics, engineering, and mathematics, such as describing physical phenomena and studying differential geometry. Asymmetric tensors can be manipulated using mathematical operations and techniques such as index notation and Einstein notation.

Mar 13, 2016

izzi wekwek

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Mar 17, 2016

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Related to Asymmetric Tensor: Definition & Examples

1. What is an asymmetric tensor?

An asymmetric tensor is a mathematical object that represents a multilinear mapping between vector spaces. It is characterized by the fact that it is not symmetric under interchange of its indices, meaning that switching the order of its arguments can result in a different value.

2. How is an asymmetric tensor different from a symmetric tensor?

An asymmetric tensor differs from a symmetric tensor in that a symmetric tensor remains unchanged when its indices are interchanged, while an asymmetric tensor does not. This means that an asymmetric tensor has fewer restrictions on its values and can take on a wider range of forms.

3. What are some examples of asymmetric tensors?

Some examples of asymmetric tensors include the stress tensor in mechanics, the electromagnetic field tensor in electromagnetism, and the Riemann curvature tensor in differential geometry. These tensors have different values depending on the order of their arguments, making them asymmetric.

4. What are the applications of asymmetric tensors?

Asymmetric tensors have many applications in physics, engineering, and mathematics. They are used to describe various physical phenomena, such as stress and strain in materials, electromagnetic fields, and the curvature of spacetime. They are also important in the study of differential geometry and its applications in fields such as general relativity and computer graphics.

5. How can asymmetric tensors be manipulated mathematically?

Asymmetric tensors can be manipulated using various mathematical operations, such as addition, multiplication, and contraction. These operations allow for the creation of new tensors from existing ones and help to simplify and solve equations involving asymmetric tensors. Additionally, techniques such as index notation and Einstein notation can be used to simplify calculations involving asymmetric tensors.