Let I be the 2 × 2 identity matrix, and M a 2 × 2 dilation matrix with M = 2I . First, we present the correlation of the scaling functions with dilation matrix M and 2I . Then by relating the properties of scaling functions with dilation matrix 2I to the properties of scaling functions with dilation matrix M , we give a parameterization of a class of bivariate nonseparable orthogonal symmetric ...

An n×n matrix is called an N 0 -matrix if all principal minors are non-positive and each entry is non-positive. In this paper, we study the partial non-combinatorially symmetric N 0 -matrix completion problems if the graph of its specified entries is a transitive tournament or a double cycle. In general, these digraphs do not have N 0 -completion. Therefore, we have given sufficient conditions ...

1. Page 2741, caption of Fig. 2: three occurrences of ‘‘commutator’’ instead of ‘‘commutor’’, i.e. the caption should read Fig. 2. Eigenvalue decomposition of the commutor for the CDFT: (a) sorted eigenvalues of the commutor T1 for N 1⁄4 128. (b) Selected symmetric and skew-symmetric eigenvectors of the commutor for k 1⁄4 0,1, 2, 3. 2. Page 2743, fourth sentence after Eq. (14): ‘‘commutator’’ i...

The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral properties. Our results are twofold: 1. We show NP-completeness for the following three problems: verifying whether a given matrix has a symmetric signing th...

In this Note we prove that the subdiscriminants of a symmetric matrix are sums of squares. This generalizes a result of [2] stating that the discriminant of a symmetric is a sum of squares and is inspired by its proof. A different, less explicit proof that the discriminant of a symmetric is a sum of squares also apear in [3]. As a consequence, we obtain an algebraic proof of the fact that all t...

1. Unitary Geometry on Exceptional Cartan Domains In 1935, E.Cartan classified all symmetric bounded domains. He prived that there exit only six types of irreducible bounded symmetric domains in C. They can be realized as follows: RI(m,n) = {Z ∈ Cmn|I − ZZ ′ > 0, Z − (m,n) matrix} RIIp = {Z ∈ Cp(p+1)/2|I − ZZ ′ > 0, Z − symmetric matric of degree p} RIIIq = {Z ∈ Cq(q−1)/2|I − ZZ ′ > 0, Z − skew...

We derive the necessary and sufficient conditions of and the expressions for the orthogonal solutions, the symmetric orthogonal solutions, and the skew-symmetric orthogonal solutions of the system of matrix equations AX B and XC D, respectively. When the matrix equations are not consistent, the least squares symmetric orthogonal solutions and the least squares skewsymmetric orthogonal solutions...

Abstract. We present a class of nonsingular matrices, the MC-matrices, and prove that the class of symmetric MC-matrices introduced by Shen, Huang and Jing [On inclusion and exclusion intervals for the real eigenvalues of real matrices. SIAM J. Matrix Anal. Appl., 31:816-830, 2009] and the class of symmetric MC-matrices are both subsets of the class of symmetric matrices with exactly one positi...

The matrix functions appear in several applications in engineering and sciences. The computation of these functions almost involved complicated theory. Thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. The aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. More...