Definition
Bra-Ket Notation
The bra-ket notation is a notation for ket-vectors, bra-vectors, inner products, and linear operators in complex inner product spaces.
A vector
is written as a ket , its dual vector as a bra . The inner product
is
- sesquilinear with the ket
as the linear side, and - the bra
as the semilinear side.
Finite Dimensions
In finite-dimensional complex vector spaces, one writes
The bra is the conjugate transpose of the ket.
Orthonormal Basis
For an orthonormal basis
The operator
Example
Example
It follows from conjugate linearity in the first argument that