Hermitian Matrix

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Related to Hermitian matrices: Unitary matrices

Hermitian matrix

[er′mish·ən ′mā·triks]
(mathematics)
A matrix which equals its conjugate transpose matrix, that is, is self-adjoint.

Hermitian Matrix

 

(or self-adjoint matrix), a matrix coincident with its adjoint, that is, a matrix such that aik= āki, where ā is the complex conjugate of the number a. If the elements of a Hermitian matrix are real, then the matrix is symmetric. A Hermitian matrix has real eigenvalues λ1, λ2, …, λn and corresponds to a linear transformation in a complex n-dimensional space that reduces to stretchings by ǀλiǀ in n mutually perpendicular directions and reflections in the planes orthogonal to the directions for which λi < 0. A bilinear form

whose coefficients form a Hermitian matrix, is called a Hermitian form. Any matrix can be written in the form A1 + iA2, where A1 and A2 are Hermitian matrices, and in the form A ∪, where A is a Hermitian matrix and U is a unitary matrix. If A and B are Hermitian matrices, then A B is a Hermitian matrix if and only if A and B commute.

References in periodicals archive ?
Here, we present an explicit construction of hives from Hermitian matrices whose proofs require little more than linear algebra.
1] be the Jordan algebra of r x r Hermitian matrices over R with composition A [omicron] B = 1/2(AB + BA) and let [SIGMA] [epsilon] [H.
It follows from Weyl's inequality that if A and B are Hermitian matrices, then
The software package handles real and complex matrices and supplies specific routines for symmetric and Hermitian matrices.
Because Hermitian matrices have only real eigenvalues and since (also by using techniques from [7]) for a given such matrix A and a given real [lambda], we succeed in evaluating all the polynomials in the sequence (1.
Here we generalize this algorithm to rational (block) Krylov subspaces, and we will show how to use and preserve symmetry when dealing with symmetric or Hermitian matrices.
It is generally admitted that convergence of the Lanczos process for Hermitian matrices is well understood.
are Hermitian matrices, we can easily conclude that F(H(T)) is the orthogonal projection of F(T) onto the real axis and F(K(T)) is the orthogonal projection of F(T) onto the imaginary axis.
Sylvester's classical law of inertia states that two Hermitian matrices A, B [member of] [C.
The aim is to compute narrow intervals for all of these entries so that we have high chances of success for a subsequent, final step which proves that all Hermitian matrices contained in X are positive definite using an approach by Rump [40].
Psarrakos [42] used this characterization to propose an algorithm to determine if a triple of Hermitian matrices is definite.