# Hermitian matrix

(redirected from Hermitian matrices)
Also found in: Encyclopedia.
Related to Hermitian matrices: Unitary matrices

## Hermitian matrix

n
(Mathematics) maths a matrix whose transpose is equal to the matrix of the complex conjugates of its entries
[C20: named after Charles Hermite (1822–1901), French mathematician]
References in periodicals archive ?
The topics include inner product spaces and orthogonality, the Jordan and Weyr canonical forms, unitary similarity and normal matrices, Hermitian matrices, vector and matrix norms, some matrix factorizations, circulant and block cycle matrices, matrices of zeros and ones, Hadamard matrices, directed graphs, non-negative matrices, and linear dynamical systems.
In Horn  the following problem was considered: characterize the possible spectra ([mu], v, [lambda]) of a triple of Hermitian matrices (M, N, L), where M + N + L = 0.
k]] Hermitian matrices, positive definiteness is equivalent to the requirement that all of its principal minors are positive, and also equivalent to the fact that all its eigenvalues are positive.
Note that the first and second terms on the right hand side of (28) are Hermitian matrices, which can be utilized to simplify the calculation.
It is also found from (10) and (11) that A and B are Hermitian matrices which can be converted to real and symmetric matrices if we replace the complex harmonics [e.
8] of 3 x 3 Hermitian matrices over the Octonions is simple with Pierce constant d = 8 but does not admit a representation.
Denote the set of all generalized Hermitian matrices by GH[C.
The core of the calculation is a series of matrix diagonalizations carried out by NAG routines designed to handle Hermitian matrices.
1], which says that if A and B are Hermitian matrices, then
The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices.
The application of this method to Hermitian matrices is essentially based on the Sturm sequence property, which means that for any given real number [lambda], the number of sign changes in the sequence of the characteristic polynomials of the principal leading submatrices of an N x N Hermitian matrix A equals the number of eigenvalues which are less than that [lambda].
We do not know either if hermitian matrices of order three are enough to represent all elements [alpha] [member of] [[?
Site: Follow: Share:
Open / Close