Hermitian matrix


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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 ?
If the n X n Hermitian matrix A has a principal submatrix Aj satisfying the following:
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.
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]).
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:
For a Hermitian matrix, the Moore's determinant is defined by specifying a certain ordering of the factors in the n!
A Hermitian matrix polynomial Q([lambda]) is definite if and only if any two (and hence all) of the following properties hold:
Banking on the fact that K[I.sup.[phi].sub.S(p,v)] is a positive Hermitian matrix, while referring to (21), we are sure that all eigenvalues of [lambda] are greater than or equal to [SNR.sup.-1] and therefore are strictly positive.
Note that, for positive semidefinite Hermitian matrix [S.sup.H]S, its condition number doubles cond(S); that is,
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
Finally, the notations d * and [lambda] * represent the main diagonal elements and eigenvalues of a Hermitian matrix, respectively.
Gupta and Luz Estela Sanchez, "A class of integral identities with Hermitian matrix argument," Proc.
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.