- In mathematics, the
complexification of a
vector space V over the
field of real
numbers (a "real
vector space")
yields a
vector space VC over the complex...
- In mathematics, the
complexification or
universal complexification of a real Lie
group is
given by a
continuous homomorphism of the
group into a complex...
- {\displaystyle {\mathfrak {sl}}(2,\mathbb {C} )} is
isomorphic to the
complexification of s o ( 3 ) {\displaystyle {\mathfrak {so}}(3)} ,
meaning the tensor...
- mutation.
Complexification: the
ability of the
system (including
evolutionary algorithm and
genotype to
phenotype mapping) to
allow complexification of the...
-
algebra g0 is
called a real form of a
complex Lie
algebra g if g is the
complexification of g0: g ≃ g 0 ⊗ R C . {\displaystyle {\mathfrak {g}}\simeq {\mathfrak...
-
infinity in the
complex projective plane that are
contained in the
complexification of
every real circle. A
point of the
complex projective plane may be...
- {\displaystyle E} can be
promoted to a
complex vector bundle, the
complexification E ⊗ C ; {\displaystyle E\otimes \mathbb {C} ;}
whose fibers are E x...
-
exactly the same as the
definition bar the
field change. Sp(n, C) is the
complexification of the real
group Sp(2n, R). Sp(2n, R) is a real, non-compact, connected...
- finite-dimensional real Lie
algebra is
semisimple if and only if its
complexification is semisimple. Each
endomorphism x of a finite-dimensional
vector space...
- Jv)+i\omega (u,v).}
Given any real
vector space V we may
define its
complexification by
extension of scalars: V C = V ⊗ R C . {\displaystyle V^{\mathbb...
