Indicial/Einstein Notation proofs

In summary, Indicial/Einstein Notation is a mathematical notation used to represent and manipulate tensors, commonly used in physics and engineering. It differs from standard notation in that repeated indices are implied to be summed over, making equations easier to manipulate. It has many applications in areas such as mechanics, electromagnetism, and general relativity. The rules for manipulating tensors in this notation include the Einstein summation convention and rules similar to those in standard calculus. To learn more about Indicial/Einstein Notation proofs, resources such as textbooks, online lectures and tutorials, and practice problems are available. It is also helpful to have a strong understanding of linear algebra and vector calculus.
  • #1
Mugged
104
0
Hello, does anyone know where I can find a proof of the following identity?

εijk εkmn = δim δjn − δin δjm
 
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  • #3
there's not too many cases to consider, when you realize if if k= any of (i,j,m,n) or i=j or m=n, the result is zero
 

FAQ: Indicial/Einstein Notation proofs

What is Indicial/Einstein Notation?

Indicial/Einstein Notation is a mathematical notation used to represent and manipulate tensors, which are mathematical objects that describe the relationship between physical quantities. It is commonly used in physics and engineering to simplify complex equations and calculations.

How is Indicial/Einstein Notation different from standard notation?

In standard notation, tensors are represented using subscript and superscript indices. However, in Indicial/Einstein Notation, the repeated indices are implied to be summed over, which reduces the number of terms in the equation and makes it easier to manipulate.

What are some common applications of Indicial/Einstein Notation?

Indicial/Einstein Notation is commonly used in areas such as mechanics, electromagnetism, and general relativity. It is particularly useful in solving problems involving vector and tensor operations, such as calculating forces and moments in rigid bodies.

What are the rules for manipulating tensors in Indicial/Einstein Notation?

The rules for manipulating tensors in Indicial/Einstein Notation include the Einstein summation convention, which states that any repeated indices are summed over. Other rules include the product rule, quotient rule, and chain rule, which are similar to those used in standard calculus.

How can I learn more about Indicial/Einstein Notation proofs?

There are many resources available for learning about Indicial/Einstein Notation proofs, including textbooks, online lectures and tutorials, and practice problems. It is also helpful to have a strong understanding of linear algebra and vector calculus to fully grasp this notation.

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