Physics, Quantum Physics, Quantum Mechanics, Quantum, Mathematics.
ket above can be written as: Where the dagger represents the hermitian conjugate/adjoint. Notice that these are just row vectors. Why we have defined the bra like this is because when we take the matrix product between a bra and a ket, we will get ⟨α|β⟩= a₁*b₁+a₂*b₂+…+aₙ*bₙ thanks to them being row