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Hello, does anyone know where I can find a proof of the following identity?
εijk εkmn = δim δjn − δin δjm
εijk εkmn = δim δjn − δin δjm
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.
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.
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.
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.
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.