Explore: Hermitian Forms

sesquilinear forms can be defined over R-modules for arbitrary rings R. Sesquilinear forms abstract and generalize the basic notion of a Hermitian form on complex

 is Hermitian ⟺ a i j = a j i ¯ {\displaystyle A{\text{ is Hermitian}}\quad \iff \quad a_{ij}={\overline {a_{ji}}}} or in matrix form: A  is Hermitian ⟺

representing the form by a matrix denoted Φ, this says that M∗ΦM = Φ. Just as for symmetric forms over the reals, Hermitian forms are determined by signature

groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional

algebra, a square matrix with complex entries is said to be skew-Hermitian or anti-Hermitian if its conjugate transpose is the negative of the original matrix

semi-characters and their associated Hermitian form ( χ , H ) {\displaystyle (\chi ,H)} , or semi-character pairs, forms a group P ( Λ ) {\displaystyle {\mathcal

with conformal dimension h {\displaystyle h} has a unique Hermitian form such that the Hermitian adjoint of L n {\displaystyle L_{n}} is L n † = L − n {\displaystyle

elements. Some of the "inner products" are symplectic forms and some are sesquilinear forms or Hermitian forms. Rather than a general field K, the instances with

anticipated by Guido Fubini a year before. The distance Study refers to is a Hermitian form on complex projective space. Since then this metric has been called

obtains the definition of positive semi-definite Hermitian form. A positive semi-definite Hermitian form ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle