# Hermitian Form

## Hermitian form

[er′mish·ən ′fȯrm] (mathematics)

A polynomial in

*n*real or complex variables where the matrix constructed from its coefficients is Hermitian.More generally, a sesquilinear form

*g*such that*g*(*x,y*) =*g*(*y,x*)for all values of the independent variables*x*and*y*, where*g*(*x,y*)is the image of*g*(*x,y*) under the automorphism of the underlying ring.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Hermitian Form

an expression of the type

where a_{kt} = ā_{tk} (ā is the complex conjugate of *a).* A matrix constructed from the coefficients of a Hermitian form is said to be Hermitian, as is a linear transformation that is defined by a Hermitian matrix. In 1854, C. Hermite investigated the representation of whole numbers by Hermitian forms for integral values of the arguments. The theory of Hermitian forms is in many respects similar to the theory of quadratic forms.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.