I have several related questions about different properties of T:

1. Given T, how do I find T*? Can someone give a simple example?

2. Given T and v (where v is a vector), how do I calculate T*(v)?

What are the best/quickest ways to tell if T is:

1.Normal

2.Self-Adjoint

3.Unitary

Is there any difference between A (a matrix) being normal/self-adjoint and T (a linear transformation) being normal/self-adjoint?

Thanks for any help!