The term "normal operator" refers to a specific type of linear operator in mathematics. Normal operators are those that commute with their adjoints, which means that the operator and its adjoint have the same eigenvectors. There are several synonyms that can be used to describe normal operators, including self-adjoint operators, Hermitian operators, and diagonalizable operators. Self-adjoint operators are those that are equal to their own adjoints, while Hermitian operators are complex operators that are equal to their own conjugate transposes. Diagonalizable operators are those that can be represented by a diagonal matrix in a certain basis. Other related terms that may be used to describe normal operators include unitary operators, which are operators that preserve the inner product of vectors, and Hermitian matrices, which are matrices that are equal to their own conjugate transposes.