A unitary matrix is a complex square matrix whose conjugate transpose is also its inverse. This means that when you multiply a unitary matrix by its conjugate transpose, the result is the identity matrix. Unitary matrices preserve the length of vectors, making them important in quantum mechanics and other fields of physics. Unitary matrices have several key properties, such as having eigenvalues that lie on the unit circle in the complex plane. They are closely related to orthogonal matrices, which are real-valued and have similar properties. Both types of matrices are used in various applications, including signal processing and computer graphics.