References in periodicals archive

If the n X n Hermitian matrix A has a principal submatrix Aj satisfying the following:

LEADING PRINCIPAL MINORS AND SEMIDEFINITENESS

the determinant of a Hermitian matrix is defined by putting det A = [rdet.sub.i] A = [cdet.sub.i] A for all i = 1, ..., n.

Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations

Actually, (37) implies that g([[phi].sub.k]) is the eigenvector associated with the minimum eigenvalue of the Hermitian matrix [V.sup.H]([[??].sub.k])[E.sub.N][E.sup.H.sub.N]V([[??].sub.k]).

Mixed Far-Field and Near-Field Source Localization Algorithm via Sparse Subarrays

For a Gaussian random Hermitian matrix [rho](M) [varies] exp - (1/2[[sigma].sup.2])Tr([M.sup.2]), the eigenvalue density obeys Wigner's semicircle law:

A Renormalisation Group Approach to the Universality of Wigner's Semicircle Law for Random Matrices with Dependent Entries

For a Hermitian matrix, the Moore's determinant is defined by specifying a certain ordering of the factors in the n!

Linear systems over Z[[Q.sub.16]] and roots of maps of some 3-complexes into [mathematical expression not reproducible]

A Hermitian matrix polynomial Q([lambda]) is definite if and only if any two (and hence all) of the following properties hold:

Effective Algorithm for Determination of the Initial Vector for the Definite Quadratic Pencil

Since (PA(e) + [(A[(e)).sup.H] P).sup.H] = PA(e) + [(A(e)).sup.H] P, then PA(e) + [(A(e)).sup.H] P is a Hermitian matrix. At the same time, since PA(e) + [(A(e)).sup.H] P = -Q, P is a real symmetric positive definite matrix, and Q is a positive definite matrix, then [[beta].sup.H] P[beta] > 0 and [[beta].sup.H] (-Q) [beta] < 0, so that

Modified Function Projective Synchronization for a Partially Linear and Fractional-Order Financial Chaotic System with Uncertain Parameters

Finally, the notations d * and [lambda] * represent the main diagonal elements and eigenvalues of a Hermitian matrix, respectively.

Capacity bounds on the ergodic capacity of distributed MIMO systems over K fading channels

We also denote by G the n x n hermitian matrix [([g.sub.ij]).sup.n.sub.i,j=1], and set [1.sub.n] for the n x n identity matrix.

Schrodinger operators with n positive eigenvalues: an explicit construction involving complex-valued potentials