Definition of Sesquilinear. Meaning of Sesquilinear. Synonyms of Sesquilinear

Here you will find one or more explanations in English for the word Sesquilinear. Also in the bottom left of the page several parts of wikipedia pages related to the word Sesquilinear and, of course, Sesquilinear synonyms and on the right images related to the word Sesquilinear.

Definition of Sesquilinear

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Meaning of Sesquilinear from wikipedia

- 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...
- 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...
- {\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...
- symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector...
- 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...
- 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...
- +{\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...
- 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...