André Lukas
Abstract
Abstract Linear maps which are singled out in the presence of a scalar product are discussed. These include the adjoint or Hermitian conjugate, Hermitian linear maps and unitary linear maps. Unitary linear maps between coordinate vectors correspond to orthogonal matrices and rotations in the real case and to unitary and special unitary matrices in the complex case.
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Abstract Linear maps which are singled out in the presence of a scalar product are discussed. These include the adjoint or Hermitian conjugate, Hermitian linear maps and unitary linear maps. Unitary linear maps between coordinate vectors correspond to orthogonal matrices and rotations in the real case and to unitary and special unitary matrices in the complex case.
Key concepts: Unitary state, Hermitian matrix, Unitary matrix, Scalar (mathematics), Mathematics, Circular ensemble, Complex conjugate, Pure mathematics