On page 187 in section “Can the Quantum Gate Matrix Be Anything?”, psi-dagger is defined as <psi^dagger| = (w0* w1*).

As per my understanding, the conjugate transpose of a bra is actually the ket, meaning <psi^dagger| = |psi> with |psi> being a column vector with entries w0 and w1 (not w0* and w1*). Am I missing something here?

(Also quoting Wikipedia here, section “Bras and kets as row and column vectors” in https://en.wikipedia.org/wiki/Bra–ket_notation: “The conjugate transpose (also called Hermitian conjugate) of a bra is the corresponding ket and vice versa”)

Thank you very much for any clarification on this topic!