- 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...
- 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...
-
symmetric or skew-symmetric
bilinear forms and
Hermitian or skew-Hermitian
sesquilinear forms defined on real,
complex and
quaternionic finite-dimensional vector...
- 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...
- +{\overline {b}}\langle x,z\rangle .} This
implies that an
inner product is a
sesquilinear form. ⟨ x + y , x + y ⟩ = ⟨ x , x ⟩ + 2 Re ( ⟨ x , y ⟩ ) + ⟨ y , y...
-
sometimes it is more
natural to
consider sesquilinear forms instead of
bilinear forms. In that case, a
given sesquilinear form ⟨·,·⟩
determines an isomorphism...
