Unitary Group
In
mathematics
, the
unitary group
of degree
n
over the
field
F
(which is either the field
\mathbb{R}
of
real numbers
or the field
\mathbb{C}
of
complex numbers
) is the
group
of
n
by
n
unitary matrices
with entries from
F
, with the group operation that of
matrix multiplication
. This is a
subgroup
of the
general linear group
\mathrm{GL}(n,F)
. In the simple case
n=1
, the group
\mathrm{U}(1)
is the
unit circle
in the complex plane, under multiplication. All the complex unitary groups contain copies of this group. If the field
F
is the field of real numbers then the unitary group coincides with the
orthogonal group
\mathrm{O}(n,\mathbb{R})
. If
F
is the field of complex numbers one usually writes
\mathrm{U}(n)
for the unitary group of degree
n
. The unitary group
\mathrm{U}(n)
is a
real
Lie group
of dimension
n^2
. The
Lie algebra
of
\mathrm{U}(n)
consists of complex
n
-by-
n
Skew-hermitian
matrices, with the
Lie bracket
given by the
commutator
.
See also
:
Special unitary group
<< Previous
Word Browser
Next >>
ladislaus bortkiewicz
fairport convention
list of inspectors of greenland
cosmological principle
bhajan
homogeneity
the fellowship of the ring (movie)
george girard
william whittingham
the two towers (movie)
metatron
laurence tomson
orthogonal group
pete fountain
center of mass
rotation group
david hartley (philosopher)
thomas holcroft
monster park
essen, germany
the pilgrim's progress
symplectic group
uncorrelated
symplectic matrix
nick griffin
soft cell
prince ferdinand philippe of france
grand duchess
jeremy taylor
special unitary group
penelope wilton
tom ford
my three sons
phar lap
tienne bonnot de condillac
bohuslav martinu
daniel massey (actor)
hall hroult process
members of the french royal families
tattoo gun
nicolas malebranche
best alternative to a negotiated agreement
spherical geometry
western blot