Quantum states are usually described using bra–ket notation, also known as Dirac notation.
In Dirac notation, a ket represents a state of a quantum system and is a vector in a complex vector space . A bra denotes a linear map , and the application of to is written as .
The ket can be represented as a column vector:
and the bra as a row vector:
In this representation, a bra next to a ket simply denotes matrix multiplication of a row vector with a column vector:
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