- 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...
-
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...
-
symmetric or skew-symmetric
bilinear forms and
Hermitian or skew-Hermitian
sesquilinear forms defined on real,
complex and
quaternionic finite-dimensional vector...
- y , {\displaystyle \mathbf {x} ^{\mathsf {T}}\mathbf {Ay} ,} and any
sesquilinear form may be
expressed as x † A y , {\displaystyle \mathbf {x} ^{\dagger...
- same way as the
canonical norm on the
continuous dual
space of H). A
sesquilinear form is a map B : H × H → C {\displaystyle \mathbb {C} } such that for...
- {\vec {k}}} .
Using the bra–ket notation, this
space is
equipped with a
sesquilinear form
defined by ⟨ k → a ; ϵ μ | k → b ; ϵ ν ⟩ = ( − η μ ν ) 2 | k → a...
- {\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...
- 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...
-
nondegenerate sesquilinear form with
companion antiautomorphism σ. Any
duality of PG(n, K) for n > 1 is
induced by a
nondegenerate sesquilinear form on the...
- to
include linear transformations of any
complex vector space with a
sesquilinear norm. Note that the
adjoint of an
operator depends on the
scalar product...
