Self-adjointness refers to a property of certain linear operators in which the operator is equal to its own adjoint. This concept is essential in understanding various mathematical structures, particularly in relation to inner product spaces, where self-adjoint operators guarantee real eigenvalues and a complete set of orthogonal eigenvectors. In the context of differential forms, the notion is connected with the Hodge star operator and the codifferential, as it influences the behavior of differential operators on Riemannian manifolds.
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