The discussion centers on the properties of the permutation symbol εijk and the classification of cyclic permutations as even or odd. It is established that cyclic permutations such as 123→231→312 yield ε123=ε231=ε312=+1, categorizing them as even. However, the confusion arises with ε132, ε213, and ε321, which are classified as odd with a value of -1. The consensus clarifies that while cyclic permutations are generally considered even, the specific arrangements of ε132, ε213, and ε321 are exceptions due to their respective transpositions.
PREREQUISITESThis discussion is beneficial for mathematicians, physicists, and students studying linear algebra or tensor analysis, particularly those interested in the properties of permutation symbols and their applications in various fields.
Oh sorry, right, but my original question is why is it written in a textbook that every cyclic permutation is even while the cyclic permutations ε132=ε213=ε321 are odd?micromass said:Why would ##\varepsilon_{321}## be even?