Given an operator $A$, $A$ is _anti-Hermitian_ or _skew-Hermitian_ if $A^\dagger = -A,$ where $^\dagger$ is the [adjoint](Adjoint.md) symbol. # Properties 1) Anti-Hermitian operators have purely, _imaginary_ eigenvalues. #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/Operators/Matrices #MathematicalFoundations/Analysis/FunctionalAnalysis