Question

Why is there a conjugate transpose in inner product not like dot product?

Answer 1

${\texttt{\huge{\purple{ANSWER :-}}}}$

If the vector is real, the complex conjugate does nothing, and the inner product is the same as the dot product . Otherwise, in the inner product and are no longer interchangeable; the conjugates are only on the first factor, Interchanging and changes the inner product's value into its complex conjugate.

Answer 2

$\huge \boxed {\bf{\green{ANSWER}}}$

If the vector is real, the complex conjugate does nothing, and the inner product is the same as the dot product . Otherwise, in the inner product and are no longer interchangeable; the conjugates are only on the first factor, . Interchanging and changes the inner product's value into its complex conjugate.