Quick question, index notation, alternating tensor.

In summary, quick question refers to a method of quickly solving complex mathematical equations using index notation. Index notation is a way of writing mathematical equations using indices or subscripts to represent repeated variables or quantities. In alternating tensors, index notation is used to represent the order of indices and the alternating nature of the tensor, simplifying the calculation process. Alternating tensors are mathematical objects that change sign when the order of its indices is changed and have various applications in physics, engineering, and computer science. They can be used to calculate quantities such as work, energy, and momentum in physical systems, as well as in solving optimization problems and analyzing data in computer science.
  • #1
binbagsss
1,259
11
Q) I am using index notation to show that ε[itex]^{0123}[/itex]=-1 given that ε[itex]_{0123}[/itex]=1.

The soluton is:

ε[itex]^{0123}[/itex]=g[itex]^{00}[/itex]g[itex]^{11}[/itex]g[itex]^{22}[/itex]g[itex]^{33}[/itex]ε[itex]_{0123}[/itex]=-ε[itex]_{0123}[/itex]

where g[itex]_{\alpha\beta}[/itex] is the metric tensor.

I am struggling to understand the last equality.

Many thanks for any assistance.
 
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  • #2
g00=-1, correct? Really, η00=-1.
 

Related to Quick question, index notation, alternating tensor.

1. What is quick question?

Quick question refers to a method of quickly solving complex mathematical equations using index notation.

2. What is index notation?

Index notation is a way of writing mathematical equations using indices or subscripts to represent repeated variables or quantities.

3. How is index notation used in alternating tensors?

In alternating tensors, index notation is used to represent the order of indices and the alternating nature of the tensor. This helps in simplifying the calculation process.

4. What are alternating tensors?

Alternating tensors are mathematical objects that change sign when the order of its indices is changed. They are commonly used in vector calculus and differential geometry.

5. How can alternating tensors be applied in real-world problems?

Alternating tensors have various applications in physics, engineering, and computer science. They can be used to calculate quantities such as work, energy, and momentum in physical systems, as well as in solving optimization problems and analyzing data in computer science.

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