A Hermitian matrix is a square matrix that is equal to its own conjugate transpose. This means that if you take the transpose of the matrix (flipping it over its diagonal) and then take the complex conjugate of each element, you will get the original matrix back. Hermitian matrices are important in various fields, including quantum mechanics and linear algebra. One key property of Hermitian matrices is that their eigenvalues are always real numbers. This characteristic makes them particularly useful in applications where real-valued solutions are needed. Additionally, the eigenvectors of a Hermitian matrix corresponding to different eigenvalues are orthogonal, which is beneficial for simplifying complex problems in mathematics and physics.