- In mathematics, a
sesquilinear form is a
generalization of a
bilinear form that, in turn, is a
generalization of the
concept of the dot
product of Euclidean...
- y , {\displaystyle \mathbf {x} ^{\mathsf {T}}\mathbf {Ay} ,} and any
sesquilinear form may be
expressed as x † A y , {\displaystyle \mathbf {x} ^{\dagger...
- {\displaystyle \mathbf {X} } and Y {\displaystyle \mathbf {Y} } is the
sesquilinear form on H 1 × H 2 {\displaystyle H_{1}\times H_{2}} (anti
linear in the...
- {\displaystyle \mathbb {R} } , conjugate-symmetry
reduces to symmetry, and
sesquilinearity reduces to bilinearity.
Hence an
inner product on a real
vector space...
- K is the
field of
complex numbers C, one is
often more
interested in
sesquilinear forms,
which are
similar to
bilinear forms but are
conjugate linear in...
-
definiteness is a
property of any
object to
which a
bilinear form or a
sesquilinear form may be
naturally ****ociated,
which is positive-definite. See, in...
-
nonzero except for the zero vector. However, the
complex dot
product is
sesquilinear rather than bilinear, as it is
conjugate linear and not
linear in a {\displaystyle...
-
equals the inverse. Over a
complex vector space, one
often works with
sesquilinear forms (conjugate-linear in one argument)
instead of
bilinear forms. The...
-
symmetric or skew-symmetric
bilinear forms and
Hermitian or skew-Hermitian
sesquilinear forms defined on real,
complex and
quaternionic finite-dimensional vector...
- y_{1}\rangle \,\langle x_{2},y_{2}\rangle \,.} This
formula then
extends by
sesquilinearity to an
inner product on H1 ⊗ H2. The
Hilbertian tensor product of H1...
