Related papers: On the absolute matrix summability factors
In this paper, we discussed the unique solvability of the two absolute value matrix equations. The unique solvability condition $\rho (\vert A^{-1} B \vert)<1$ is provided for the generalized absolute value matrix equation (GAVME) $AX + B…
We provide new sufficient conditions under which Ryser's conjecture holds.
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
In this paper, we present a new necessary and sufficient condition for which the supremum exists with respect to the logic order. Moreover, we give out a new and much simpler representation of the supremum with respect to the order, our…
We prove that all Mathieu groups, some linear, and unitary groups are factorizable.
We give a necessary and sufficient condition for a type of generalized power series to be algebraic over the ring of power series with coefficients in a finite field. This result extend a classical theorem of Huang-Stefanescu.
Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof.…
This paper establishes that every positive-definite matrix can be written as a positive linear combination of outer products of integer-valued vectors whose entries are bounded by the geometric mean of the condition number and the dimension…
We prove that certain vector bundles over surfaces are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to $\det(E)$). This result is a higher-rank version of a theorem…
A positive definiteness criterion and, under the additional conditions, a nonnegativity criterion for a self-adjoint continuous operator matrix, acting in product of an arbitrary number of real separable Hilbert spaces, are obtained. As…
It is established that if a time series satisfies the Berman condition, and another related (summability) condition, the result of filtering that series through a certain type of filter also satisfies the two conditions. In particular it…
This paper derives sufficient conditions for superconvergence of sums of bounded free random variables and provides an estimate for the rate of superconvergence.
We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition…
Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a…
We present a necessary and sufficient condition for the separability of multipartite quantum states, this criterion also tells us how to write a multipartite separable state as a convex sum of separable pure states. To work out this…
We propose a sufficient condition of the convergence of a generalized power series formally satisfying an algebraic (polynomial) ordinary differential equation. The proof is based on the majorant method.
A simple geometric condition is sufficient for analytic hypoellipticity of sums of squares of two vector fields in ${\mathbb R}^2$. This condition is proved to be necessary for generic vector fields and for various special cases, and to be…
In the paper, a simple condition guaranteing the finiteness property for a bounded set of matrices is presented. Given a bounded set S of real or complex matrices, it is shown that existence of a sequence of matrix products such that the…
Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these…
We determine a necessary and sufficient condition for a polynomial over an algebraically closed field $k$ to induce a surjective map on matrix algebras $M_n(k)$ for $n \ge 2$. The criterion is given in terms of critical points and uses…