## Basic Matrix Features

 Relations Name matrix elements $$A = A^{T}$$ symmetric $$a_{ij} = a_{ji}$$ $$A = \left (A^{T} \right )^{-1}$$ real orthogonal $$\sum_k a_{ik} a_{jk} = \sum_k a_{ki} a_{kj} = \delta_{ij}$$ $$A = A^{ * }$$ real matrix $$a_{ij} = a_{ij}^{ * }$$ $$A = A^{\dagger}$$ hermitian $$a_{ij} = a_{ji}^{ * }$$ $$A = \left (A^{\dagger} \right )^{-1}$$ unitary $$\sum_k a_{ik} a_{jk}^{ * } = \sum_k a_{ki}^{ * } a_{kj} = \delta_{ij}$$