In mathematics and physics, a matrix is called Hermitian if it is equal to its own conjugate transpose. This means that for a Hermitian matrix, the element in the i-th row and j-th column is the complex conjugate of the element in the j-th row and i-th column. Hermitian matrices have real eigenvalues and their eigenvectors can be chosen to be orthogonal. Hermitian operators play a crucial role in quantum mechanics, where they represent observable physical quantities. The properties of Hermitian matrices ensure that measurements yield real values, making them essential for the mathematical formulation of quantum systems.