The Jordan product of two n x n matrices A and B, defined as (AB + BA)/2, is commutative but not associative. To demonstrate commutativity, one must show that A*B = B*A, while for associativity, it is necessary to prove that A*(B*C) ≠ (A*B)*C. The discussion provides a clear method for expanding these expressions to verify the properties of the Jordan product.
PREREQUISITESStudents of linear algebra, mathematicians exploring matrix theory, and educators teaching properties of matrix operations.
Thank you so much for the help. I figured out this question and the other Jordan Product questions from your advice.JeSuisConf said:/edit: deleted answer.
For associativity, just write out A*B and B*A and expand. For commutivity, write out A*(B*C) and (A*B)*C, and if what you get when you expand the two things is not the same, then you have shown what you wanted.