Bra-ket notation constitutes a rigorous formalism within quantum mechanics for representing state vectors in abstract Hilbert spaces using Dirac's symbolic syntax. The core principle defines the dual space relationship where kets denote column vectors and bras denote row vector functionals, establishing inner products as scalar amplitudes via linearity rules. This framework provides an agnostic representation of physical states applicable across all quantum systems without reference to specific spatial coordinates or bases until explicit projection is performed.
Introduces kets, bras, and inner products as the compact vector notation of quantum mechanics.