Unitary matrix
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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:
1) ;
2) ;
3) ;
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.
Comments
References
[a1] | W. Noll, "Finite dimensional spaces" , M. Nijhoff (1987) pp. 63 |
[a2] | W.H. Greub, "Linear algebra" , Springer (1975) pp. 329 |
How to Cite This Entry:
Unitary matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unitary_matrix&oldid=13327
Unitary matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unitary_matrix&oldid=13327
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article