Related papers: Structured Singular values on some generalized sto…
The structured pseudospectra of a matrix A are sets of complex numbers that are eigenvalues of matrices X which are near to A and have the same entries as A at a fixed set of places. The sum of multiplicities of the eigenvalues of X inside…
A generalized matrix function is a generalization of determinant and permanent function. In this paper, we introduced the formula for the value of a generalized matrix function of a linear sum of permutation matrices. We show that a linear…
In this paper we investigate congruence relationships of particular finite generalized harmonic numbers sums. We suggest more transparent and simpler method to analyse these sums and present several additional results for certain special…
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…
A counter-example to lower bounds for the singular values of the sum of two matrices in [1] and [2] is given. Correct forms of the bounds are pointed out.
We prove that the squared singular values of a fixed matrix multiplied with a truncation of a Haar distributed unitary matrix are distributed by a polynomial ensemble. This result is applied to a multiplication of a truncated unitary matrix…
This paper deals with strong structural controllability of linear structured systems in which the system matrices are given by zero/nonzero/arbitrary pattern matrices. Instead of assuming that the nonzero and arbitrary entries of the system…
Graph matrices are a type of matrix which has played a crucial role in analyzing the sum of squares hierarchy on average case problems. However, except for rough norm bounds, little is known about graph matrices. In this paper, we take a…
The standard theorem for regular stochastic matrices is generalized to matrices with no sign restriction on the entries. The condition that column sums be equal to 1 is kept, but the regularity condition is replaced by a condition on the…
A new property, the strong singular value property, is introduced, developed, and utilized to study the problem of which lists of nonnegative real numbers occur as the singular values of a matrix with a prescribed zero-nonzero pattern.
In this paper, we derive new model formulations for computing generalized singular values of a Grassman matrix pair. These new formulations make use of truncated filter matrices to locate the $i$-th generalized singular value of a Grassman…
In this article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values…
In this paper, we give a new discovery of conversion of generalized singular values. New formulation is proposed.
Concatenating matrices is a common technique for uncovering shared structures in data through singular value decomposition (SVD) and low-rank approximations. The fundamental question arises: How does the singular value spectrum of the…
In this paper, we investigate extreme singular values of the analysis matrix of a Gabor frame $(g, \Lambda)$ with a random window $g$. Columns of such matrices are time and frequency shifts of $g$, and $\Lambda\subset…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
We consider a generalized Gauss sum supported on matrices over a number field. We evaluate this Gauss sum and relate it to the number of totally isotropic subspaces of related quadratic spaces. Then we consider a further generalization of…
A real quadratic matrix is generalized doubly stochastic (g.d.s.) if all of its row sums and column sums equal one. We propose numerically stable methods for generating such matrices having possibly orthogonality property or/and satisfying…
In this note, we give a simple method for computing the column sums of the Sonnenschein summability matrices.
We clarify the confusion in the expression of the static structure factor S(k) in the study of condensed matters and discuss its explicit form that can be directly used in calculations and computer simulations.