11. The importance of symmetric and antisymmetric states is ultimately based on empirical evidence. 12. The corresponding eigenvectors are the symmetric and antisymmetric states: 13. Similarly one can express elementary symmetric polynomials via traces over antisymmetric tensor powers. 14. Particles which exhibit antisymmetric states are called fermions. 15. Here juxtaposition is symmetric respectively antisymmetric multiplication in the symmetric and antisymmetric tensor algebra. 16. Here juxtaposition is symmetric respectively antisymmetric multiplication in the symmetric and antisymmetric tensor algebra. 17. Where is an arbitrary antisymmetric tensor in indices. 18. They are antisymmetric with respect to the other. 19. In other words, iteration is antisymmetric , and thus, a partial order. 20. :The tensors that show up in physics are usually either symmetric or antisymmetric .
