On the LU Factorization of M-Matrices.
On the -th roots of a complex matrix.
On the matrices of central linear mappings
We show that a central linear mapping of a projectively embedded Euclidean -space onto a projectively embedded Euclidean -space is decomposable into a central projection followed by a similarity if, and only if, the least singular value of a certain matrix has multiplicity . This matrix is arising, by a simple manipulation, from a matrix describing the given mapping in terms of homogeneous Cartesian coordinates.
On the matrix equation over finite fields.
On the matrix form of Kronecker lemma
A matrix generalization of Kronecker's lemma is presented with assumptions that make it possible not only the unboundedness of the condition number considered by Anderson and Moore (1976) but also other sequences of real matrices, not necessarily monotone increasing, symmetric and nonnegative definite. A useful matrix decomposition and a well-known equivalent result about convergent series are used in this generalization.
On the matrix negative Pell equation
Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) with d ∈ N for nonsingular , i=1,...,n.
On the matrix norm subordinate to the Hölder norm.
On the maximal subgroup of the sandwich semigroup of generalized circulant Boolean matrices
Let be a positive integer, and the set of all -circulant matrices over the Boolean algebra , . For any fixed -circulant matrix () in , we define an operation “” in as follows: for any in , where is the usual product of Boolean matrices. Then is a semigroup. We denote this semigroup by and call it the sandwich semigroup of generalized circulant...
On the Maximum Eigenvalue of a Reducible Non-Negative Real Matrix.
On the maximum positive semi-definite nullity and the cycle matroid of graphs.
On the maximum row and column sum norm of GCD and related matrices.
On the Maximum Value of a Class of Determinants
On the minimum rank of not necessarily symmetric matrices: a preliminary study.
On the minimum vector rank of multigraphs.
On the Monotonity of Incomplete Factorization.
On the necessary and sufficient condition for a set of matrices to commute and some further linked results.
On the Nonflatness of Analytic Tensor Product.
On the Nonnegativity of XX* and its Relevance in Econometrics.
On the non-quadraticity of values of the q-exponential function and related q-series
On the optimality and sharpness of Laguerre's lower bound on the smallest eigenvalue of a symmetric positive definite matrix
Lower bounds on the smallest eigenvalue of a symmetric positive definite matrix play an important role in condition number estimation and in iterative methods for singular value computation. In particular, the bounds based on and have attracted attention recently, because they can be computed in operations when is tridiagonal. In this paper, we focus on these bounds and investigate their properties in detail. First, we consider the problem of finding the optimal bound that can be computed...