In this note we characterize polynomial numerical hulls of matrices A 2 Mn such that A 2 is Hermitian. Also, we consider normal matrices A 2 Mn whose k th power are semidenite. For such matrices we show that V k (A) = (A).
For any n-by-n complex matrix A, we use the joint numerical range W (A, A 2 , . . . , A k ) to study the polynomial numerical hull of order k of A, denoted by V k (A). We give an analytic description of V 2 (A) when A is normal. The... more
In this paper we study the problem of complete stagnation of the generalized minimum residual (GMRES) method for normal matrices. We first characterize all n × n nonsingular normal matrices A such that GMRES(A, b) stagnates completely for... more
We formulate and study a class of U (N )-invariant quantum mechanical models of large normal matrices with arbitrary rotation-invariant matrix potentials. We concentrate on the U (N ) singlet sector of these models. In the particular case... more
Given a {0, 1, * }-matrix M , a minimal M-obstruction is a digraph D such that D is not M-partitionable, but every proper induced subdigraph of D is. In this note we present a list of all the M-obstructions for every 2 × 2 matrix M.... more
In this note, analytic description of V 3 (A) is given for normal matrices of the form A = A 1 ⊕ iA 2 or A = A 1 ⊕ e i 2π 3 A 2 ⊕ e i 4π 3 A 3 , where A 1 , A 2 , A 3 are Hermitian matrices. The new concept "k th roots of a convex set" is... more
The notion of polynomial numerical hull was introduced by O. Nevanlinna [Convergence of Iteration for linear equations, Birkhäuser, 1993]. In this note we determine the polynomial numerical hulls of matrices of the form A = A 1 ⊕ iA 2 ,... more
The concept of nilpotency for a topological space is a generalization of simple connectivity. That it is a fruitful generalization was shown by Dror, Kan, Bousfield, Hilton, and others. In 1977 Brown and Kahn proved that the dimension of... more
Sharp estimates for the absolute values of entries of matrix valued functions of finite and infinite matrices are derived. These estimates give us bounds for various norms of matrix valued functions. Applications of the obtained estimates... more
The Hoifman-Wielandt inequality, which gives a bound for the distance between the spectra of two normal matrices, is generalized to normal operators A, B on a separable Hubert space, such that A-B is Hilbert-Schmidt.
We revisit the normality preserving augmentation of normal matrices studied by Ikramov and Elsner in 1998 and complement their results by showing how the eigenvalues of the original matrix are perturbed by the augmentation. Moreover, we... more
In this article, tracial numerical ranges associated with matrices in an indefinite inner product space are investigated. The boundary equations of these sets are obtained and the case of the boundary being a polygon is studied. As an... more
Let A be a normal matrix and consider the polygon NR[A] = {x * Ax: x = 1}. If υ * Aυ ∈ int NR[A], a projector matrix P υ is defined such that NR[P * υ AP υ ] is supported by all or some edges of a polygon.
In this paper, we study a compression of normal matrices and matrix polynomials with respect to a given vector and its orthogonal complement. The numerical range of this compression satisfies special boundary properties, which are... more
In this paper, we study a particular class of block matrices placing an emphasis on their spectral properties. Some related applications are then presented.
We extend generalized projectors (introduced by Groß and Trenkler in [Linear Algebra Appl. (1997) 264]) to k-generalized projectors and we characterize them obtaining results in the aforesaid paper as a consequence. Moreover, we list all... more
We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the... more
In the application of the modal decoupling method, questions arise as to why the nonnormal matrices LC and CL are diagonalizable. Is the definition of the characteristic impedance matrix Z , unique? Is it possible to normalize current and... more
Let A, C ∈ M n , the algebra of n × n complex matrices. The set of complex numbers C (A) = {det (A − U CU *) : U * U = I n } is the C-determinantal range of A. In this note, it is proved that C (A) is an elliptical disc for A, C ∈ M 2. A... more
Several of Chandler's paternal ancestors traveled from England to America on the Mayflower. The name Davis goes back to Dolor Davis, who landed in 1634. On his mother's side, Chandler's ancestors immigrated to America from Germany and... more
We exhibit equivalent conditions for subspaces of an inner product space to be isoclinic, including a characterization based on the classical notion of canonical angles. We identify a connection with quantum error correction, showing that... more
In the application of the modal decoupling method, questions arise as to why the nonnormal matrices LC and CL are diagonalizable. Is the definition of the characteristic impedance matrix Z , unique? Is it possible to normalize current and... more
The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For a noisy quantum channel, a quantum error correcting code of dimension k exists, if and only if the... more
In this note, analytic description of V 3 (A) is given for normal matrices of the form A = A 1 ⊕ iA 2 or A = A 1 ⊕ e i 2π 3 A 2 ⊕ e i 4π 3 A 3 , where A 1 , A 2 , A 3 are Hermitian matrices. The new concept "k th roots of a convex set" is... more
Krylov subspace methods are strongly related to polynomial spaces and their convergence analysis can often be naturally derived from approximation theory. Analyses of this type lead to discrete min-max approximation problems over the... more
For any operator M acting on an N-dimensional Hilbert space HN we introduce its numerical shadow, which is a probability measure on the complex plane supported by the numerical range of M. The shadow of M at point z is defined as the... more
The fact that given complex n × n matrices A and B are (or are not) unitarily similar can be verified with the help of the Specht-Pearcy criterion. Its application, however, involves a huge amount of computational work; to get a positive... more
The dynamical effects of the QCD-based gluon field overlap factor \emph{f} ($\exp(-b_{s} k_{f}\sum_{i<j} r_{ij}^{2})$) has been seen for the scattering process of $D^{o}\bar{D}_{o}^{*}\longrightarrow\omega J/\psi$. The value used for... more
Krylov subspace methods are strongly related to polynomial spaces and their convergence analysis can often be naturally derived from approximation theory. Analyses of this type lead to discrete min-max approximation problems over the... more
Business processes continue to play an important role in today’s service-oriented enterprise computing systems. Mining, discovering, and integrating process-oriented services has attracted growing attention in the recent years. In this... more
In the application of the modal decoupling method, questions arise as to why the nonnormal matrices LC and CL are diagonalizable. Is the definition of the characteristic impedance matrix Z , unique? Is it possible to normalize current and... more
Exploring the idea that equation for radial wave function must be compatible with the full Schrodinger equation, a boundary condition () 0 u 0 = is derived.
In this paper we study the problem of complete stagnation of the generalized minimum residual (GMRES) method for normal matrices. We first characterize all n × n nonsingular normal matrices A such that GMRES(A, b) stagnates completely for... more
Let A be an n × n normal matrix, whose numerical range NR[A] is a k-polygon. If a unit vector v ∈ W ⊆ C n , with dimW = k and the point v * Av ∈ Int NR[A], then NR[A] is circumscribed to NR[P * AP], where P is an n × (k − 1) isometry of... more
In this paper, we study a compression of normal matrices and matrix polynomials with respect to a given vector and its orthogonal complement. The numerical range of this compression satisfies special boundary properties, which are... more
For an n  n normal matrix A, whose numerical range NR[A] is a k-polygon (k 6 n), an n  (k À 1) isometry matrix P is constructed by a unit vector t 2 C n , and NR[P*AP] is inscribed to NR[A]. In this paper, using the notations of... more
Given a symmetric m by m matrix M over 0, 1, * , the M-partition problem asks whether or not an input graph G can be partitioned into m parts corresponding to the rows (and columns) of M so that two distinct vertices from parts i and j... more
This paper considers an orthogonal amplify-andforward (OAF) protocol for cooperative relay communication over Rayleigh-fading channels in which the intermediate relays are permitted to linearly transform the received signal and where the... more
When can an (nk) × (nk) normal matrix B be imbedded in an n × n normal matrix A? This question was studied for the first time 50 years ago by Ky Fan and Gordon Pall, who gave the complete answer in the case k = 1. Since then, a few... more
Let A be a normal matrix and consider the polygon is supported by all or some edges of a polygon.
A new parallel division of polynomials by a common separable divisor over a perfect field is presented and this is done by expressing the remainders as derivatives of a unique polynomial. In order to get this result, a novel variant... more
For any operator M acting on an N-dimensional Hilbert space HN we introduce its numerical shadow, which is a probability measure on the complex plane supported by the numerical range of M. The shadow of M at point z is defined as the... more
Hadamard&amp;amp;amp;amp;amp;#x27;s determinant theorem is used to obtain an upper bound for the modulus of the determinant of the sum of two normal matrices in terms of their eigenvalues. This bound is compared with another given by... more
Received by the editors December 28, 2008. Accepted for publication April 17, 2009. Handling Editor: Bit-Shun Tam. Department of Mathematics, Vali-E-Asr University of Rafsanjan, Rafsanjan, Iran ([email protected], [email protected]).... more
For a self-adjoint linear operator with discrete spectrum or a Hermitian matrix the "extreme" eigenvalues define the boundaries of clusters in the spectrum of real eigenvalues. The outer extreme ones are the largest and the smallest... more
A polynomial preconditioner to an invertible matrix is constructed from the (near) best uniform polynomial approximation to the function 1/x on the eigenvalues of the matrix. The preconditioner is developed using symmetric matrices whose... more
In this paper, we study a compression of normal matrices and ma-trix polynomials with respect to a given vector and its orthogonal complement. The numerical range of this compression satisfies special boundary properties, which are... more