Take the 2-minute tour ×  I am trying to define some operators I
used frequently.For example, I defined a KroneckerProduct
operator as $ \otimes $ as follows:  a_$ \otimes $b_:=a.b-b.a
and this works fine.  Then I want to define a commutator used in
quantum mechanics act like follows: $${\left[ {a,b} \right]_ - }
= a.b - b.a$$ $${\left[ {a,b} \right]_ + } = a.b + b.a$$ where a
and b are matrix.  So I naively write the definition in
matheamtica as follows:  $${\left[ {a{\rm{\_}},b{\rm{\_}}}
\right]_ - }: = a.b - b.a$$ $${\left[ {a{\rm{\_}},b{\rm{\_}}}
\right]_ + }: = a.b + b.a$$  But this will not work.  1.So how
to define commutator in this form (appearance)?  2.and why the
definition for a_$\otimes$b_ hold, the similar definition for
commutator [a_,b_]not hold?  There is another question which
actually should create another post. But I choose just to add it
here.  If I defined the KroneckerProduct as the operator
[CircleTimes] in the way I did, then I found that in parallel
computing, I can't simply distrib