A normal matrix is a type of square matrix that commutes with its conjugate transpose. This means that if A is a normal matrix, then A A^* = A^* A , where A^* represents the conjugate transpose of A . Normal matrices include important classes such as Hermitian matrices, unitary matrices, and symmetric matrices. Normal matrices have several useful properties, including the ability to be diagonalized by a unitary matrix. This means that any normal matrix can be expressed in a form where its eigenvalues are on the diagonal, making it easier to analyze and compute. The spectral theorem is a key result related to normal matrices, providing insights into their structure and behavior.