Question

Suppose a in R^3. Define A in L(R^3) by Av = a cross v
a) find adjoint A^*, assuming that R63 is equipped with the standard dot product
b) Is A a normal operator?
Please help

Answer 1

to find \(A^*\) I need start from definition (\(Av, y) = (v,A^*y)\)

Answer 2

However, I lost at replace Av in the definition
Av = a x v
so that (a x v, y ) = (a, y)x (v,y) , then? x stands for cross product