A unitary matrix is a complex square matrix whose conjugate transpose is also its inverse. This means that when a unitary matrix is multiplied by its conjugate transpose, the result is the identity matrix. Unitary matrices preserve the length of vectors, making them important in various fields, including quantum mechanics and signal processing. In mathematical terms, if U is a unitary matrix, then U^* U = I , where U^* is the conjugate transpose of U and I is the identity matrix. Unitary matrices are analogous to orthogonal matrices in real number spaces, which also preserve vector lengths but only involve real numbers.