A square matrix over the field of complex numbers, whose rows form an orthonormal system, i.e.
. In a unitary space, transformation from one orthonormal basis to another is accomplished by a unitary matrix. The matrix of a unitary transformation relative to an orthonormal basis is also (called) a unitary matrix. A square matrix with complex entries is unitary if and only if it satisfies any of the following conditions:
4) the columns of form an orthonormal system (here is the conjugate transposed of ).
The determinant of a unitary matrix is a complex number of modulus one.
|[a1]||W. Noll, "Finite dimensional spaces" , M. Nijhoff (1987) pp. 63|
|[a2]||W.H. Greub, "Linear algebra" , Springer (1975) pp. 329|
Unitary matrix. O.A. Ivanova (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Unitary_matrix&oldid=13327