Question

Why is the adjoint operation in HW5 defined opposite of the adjoint in class?

Answer 1

I believe this is only because Dr. Vela defined it incorrectly in class. I believe the definition of transpose is the one given on the homework. However...be careful how you use it.

Let's define in the hammer example the transformation from base to head as \[h = g^{A}_{A'}\] and we have some transformation of the base \[g^A_B\]If we want the transformation of the head, we can see by arranging coefficients that \[g^{A'}_{B'} = g^{A'}_A*g^A_B*g^A_{A'} \]You can see that the operation we want is inv(h)*g*h, which can be shown to equal the inv(adjoint). If you define\[h = g^{A'}_A\]then the standard form of the adjoint you coded would be the proper one to use.