The relationship between the Hermitian matrix H and an alternative real symmetric matrix is given, together with the appropriate criteria for root location with respect to the imaginary axis. Also discussed are the form of the inverse of H and applications to Sylvester-form matrices, the reduced ...
Hermitian matrices have the following nice property. Proposition Let be a matrix. If is Hermitian, then all its eigenvalues are real (i.e., their complex parts are zero). ProofAll the eigenvalues of a symmetric real matrix are realIf a real matrix is symmetric (i.e., ), then it is ...
For a Hermitian matrix H with nonsingular principal submatrix A, it is shown that the eigenvalues of the Moore-Penrose inverse of the Schur complement (H/A) of A in H interlace the eigenvalues of the Moore-Penrose inverse of H. Moreover, if H is semidefinite, it is shown that the eige...
We consider random non-hermitian matrices in the large- N limit. The power of analytic function theory cannot be brought to bear directly to analyze non-h... J Feinberg,A Zee - 《Nuclear Physics B》 被引量: 188发表: 1997年 Green's Functions in Non-hermitian Random Matrix Models In this...
Within the three-neutrino paradigm, all the neutrino EM properties are Hermitian matrices. In the Standard Model (SM) of particle physics, the tree-level coupling between neutrino and photon is zero [4] while the loop-induced electromagnetic couplings are highly suppressed. While the neu- trino ...
to obtain a new proof of a result that these 0 F 1 functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arbitrary generalized ( r F s ) functions of two matrix arguments and to the generalized hypergeometric functions of Hermitian matrix arguments....
The following lemma now captures how A acting simultaneously on the row and column space of an Hermitian matrix distorts its nuclear norm. To this end, let ⁎‖X‖⁎ denote the nuclear norm of X, i.e., the sum of the eigenvalues of X and 〈⋅,⋅〉 denote the Hilbert-Schmidt ...
denotes the Hermitian conjugate. The disordered pattern is described by tij, which is determined by the spatial distance dij between the ith and jth lattice sites. For generality, we consider all orders of hopping between lattice sites by defining the near-field hopping condition tij = t0...
In the first part of the present paper, we aim at specifying conditions under which certain properties of P hold also for S and T when P is an idempotent matrix (i.e., represents a projector) or a Hermitian idempotent matrix (i.e., represents an orthogonal projector). Among the ...
In addition, ta (a = 1, 2, . . . , N 2 − 1) are the generators of the group SU(N ) in the fundamental representation. The matrices ta are hermitian and traceless, generating the closed algebra [ta, tb] = i f abctc, (2.2) where f abc are the totally antisymmetric ...