Anti-Symmetric Tensor: Solving for 'a' in W[ijWk]l=aW[ijWkl]

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In summary, an anti-symmetric tensor is a mathematical object used in physics and mathematics to represent quantities that change sign when two indices are interchanged. It differs from symmetric tensors in that swapping indices results in a negative sign. Real-life applications include mechanics, electromagnetism, and fluid dynamics. It is related to the cross product and not all tensors are anti-symmetric.
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all indices are subscripts W[ijWk]l=aW[ijWkl]
what will be the value of ''a''?
Wij is the ndim-tensor with ij subscripts...
if we include the index 'l' in anti-symmetric, then what would be the value of ''a''...where ''a'' is combinatorial factor...
 
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please help...anti-symmetric tensor...

NAZIMTUFAIL said:
if W[ijWk]l=aW[ijWkl]
ijkl are subscripts as well as indices.
W is vortacity. what will be the value of ''a''?
if we include the index 'l' in anti-symmetric competition , then what would be the value of ''a''...where ''a'' is combinatorial factor...
[] brackets shows the anti-symmetric notations..
 

FAQ: Anti-Symmetric Tensor: Solving for 'a' in W[ijWk]l=aW[ijWkl]

What is an anti-symmetric tensor?

An anti-symmetric tensor is a type of mathematical object that is used in physics and mathematics to represent quantities that behave differently under certain transformations. It is a multi-dimensional array of numbers that has a specific property: if any two indices are interchanged, the sign of the tensor changes.

How does an anti-symmetric tensor differ from a symmetric tensor?

An anti-symmetric tensor is similar to a symmetric tensor in that both have the same number of components and follow specific transformation rules. However, the main difference is that in an anti-symmetric tensor, swapping any two indices results in a negative sign, while in a symmetric tensor, the sign remains the same.

What are some real-life applications of anti-symmetric tensors?

Anti-symmetric tensors are commonly used in mechanics, electromagnetism, and general relativity to describe physical quantities such as angular momentum, magnetic fields, and stress tensors. They are also used in the study of fluid dynamics and quantum mechanics.

How are anti-symmetric tensors related to the cross product?

The cross product of two vectors in three-dimensional space can be represented as an anti-symmetric tensor. This is because the cross product has the property of being anti-symmetric, meaning that swapping the order of the vectors changes the sign of the resulting vector. In this way, the anti-symmetric tensor encapsulates the same information as the cross product.

Are all tensors anti-symmetric?

No, not all tensors are anti-symmetric. Tensors can have various properties, including symmetry, skew-symmetry, and anti-symmetry. An anti-symmetric tensor is a specific type of tensor that follows a particular transformation rule, while other tensors may have different properties and behave differently under transformations.

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