Related papers: M-matrices satisfy Newton's inequalities

Several subadditivity results and conjectures are given for matrices (or operators), block-matrices, concave functions and norms.

The Deligne-Simpson problem in the multiplicative version is formulated like this: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\in SL(n,{\bf C})$ so that there exist irreducible $(p+1)$-tuples…

This paper investigates the Smith normal form equivalence problem for multivariate polynomial matrices. Using methods from matrix theory and polynomial ideal theory, we prove that Frost and Storey's 1978 conjecture holds for a broad class…

Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…

For each positive integer $n \geq 4$, we give an inequality satisfied by rank functions of arrangements of $n$ subspaces. When $n=4$ we recover Ingleton's inequality; for higher $n$ the inequalities are all new. These inequalities can be…

Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…

We consider certain functional identities on the matrix algebra $M_n$ that are defined similarly as the trace identities, except that the "coefficients" are arbitrary polynomials, not necessarily those expressible by the traces. The main…

This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…

In this paper, we extend the classical Newton-Maclaurin inequalities to functions $S_{k;s}(x)=E_k(x)+\dsum_{i=1}^s \al_i E_{k-i}(x)$, which are formed by linear combinations of multiple basic symmetric mean. We proved that when the…

Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…

We present a formula for the trace of any symmetric power of a $n\times n$ matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and…

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…

A general class of Newton algorithms on Gra{\ss}mann and Lagrange-Gra{\ss}mann manifolds is introduced, that depends on an arbitrary pair of local coordinates. Local quadratic convergence of the algorithm is shown under a suitable condition…

The equivalence of multidimensional systems is closely related to the reduction of multivariate polynomial matrices, with the Smith normal form of matrices playing a key role. So far, the problem of reducing multivariate polynomial matrices…

When doubly-affine matrices such as Latin and magic squares with a single non-zero eigenvalue are powered up they become constant matrices after a few steps. The process of compounding squares of orders m and n can then be used to generate…

There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…

Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certificate, in terms of Linear Matrix Inequalities and Bilinear…

We prove the existence of gaps between all the different classes of matrix monotone functions defined on an interval, provided the interval is non trivial and different from the whole real line. We then show how matrix monotone functions…

One may identify the general properties of the neutrino mass matrix by generating many random mass matrices and testing them against the results of the neutrino experiments.

Using the theory of equitable decompositions it is possible to decompose a matrix $M$ appropriately associated with a given graph. The result is a collection of smaller matrices whose collective eigenvalues are the same as the eigenvalues…