Yes they can be, the two definitions are not related.
An antisymmetric relation on a set is a binary relation ( R ) such that if ( aRb ) and ( bRa ) then ( a = b ). For a set with ( n ) elements, there are ( n(n-1)/2 ) pairs where ( a \neq b ), and each of these pairs can independently be included or excluded from the relation. Additionally, each element can relate to itself, contributing ( 2^n ) possibilities for self-relations. Therefore, the total number of antisymmetric relations is ( 2^{n(n-1)/2} ).
No, but sometimes "average" means "mean" - when it doesn't mean median, geometric mean, or something else entirely.
The answer will depend on who you mean by HE.The answer will depend on who you mean by HE.The answer will depend on who you mean by HE.The answer will depend on who you mean by HE.
See mean-8. Or get a dictionary.
An antisymmetry is the mathematical condition of being antisymmetric.
No it is not.
Symmetric wave functions remain unchanged when particles are exchanged, while antisymmetric wave functions change sign when particles are exchanged.
An antisymmetrization is an act of making something antisymmetric.
A bivector is a mathematical term for an antisymmetric tensor of second rank.
Yes, identical fermions have antisymmetric wavefunctions. Identical bosons have symmetric -- look up Spin Statistics in any Standard Field Theory text.
Yes they can be, the two definitions are not related.
An antisymmetric relation on a set is a binary relation ( R ) such that if ( aRb ) and ( bRa ) then ( a = b ). For a set with ( n ) elements, there are ( n(n-1)/2 ) pairs where ( a \neq b ), and each of these pairs can independently be included or excluded from the relation. Additionally, each element can relate to itself, contributing ( 2^n ) possibilities for self-relations. Therefore, the total number of antisymmetric relations is ( 2^{n(n-1)/2} ).
Well the one definition of asymmetric is: anything that fails to be symmetric.So a possible sentence if your working with math could be:The equation is clearly asymmetric.
It is a partially ordered set. That means it is a set with the following properties: a binary relation that is 1. reflexive 2. antisymmetric 3. transitive a totally ordered set has totality which means for every a and b in the set, a< or equal to b or b< or equal to a. Not the case in a poset. So a partial order does NOT have totality.
The wave function of a two-electron system with total spin one can be expressed using the symmetric spin wave function, taking into account both spatial and spin components. This wave function should satisfy the Pauli exclusion principle and be antisymmetric under exchange of electron coordinates.
For lithium with identical electrons, the ground state wave function is a symmetric combination of the individual electron wave functions. This means that the overall wave function is symmetric under exchange of the two identical electrons. This symmetric combination arises from the requirement that the total wave function must be antisymmetric due to the Pauli exclusion principle.