Where does the transpose come from in the work inner product equation

[princejan7]

Homework Statement

http://postimg.org/image/lgphyvggz/

Homework Equations

The Attempt at a Solution

can someone explain where that transpose came from in (3.3)?

 

[HallsofIvy]

In any inner product space the "transpose" (more generally, "adjoint") of a linear operator is defined by $<u, Av>= <A^Tu, v>$.

3.3 is just saying that $<Au, Av>= <A^T(Au), v>$