Non-Homogeneous Markov Chains: Tail Idempotents, Tail Sigma-Fields and Basis.
Non-intersecting, simple, symmetric random walks and the extended Hahn kernel
We show using non-intersecting paths, that a random rhombus tiling of a hexagon, or a boxed planar partition, is described by a determinantal point process given by an extended Hahn kernel.
Nonnegative definite hermitian matrices with increasing principal minors
A nonnegative definite hermitian m × m matrix A≠0 has increasing principal minors if det A[I] ≤ det A[J] for I⊂J, where det A[I] is the principal minor of A based on rows and columns in the set I ⊆ {1,...,m}. For m > 1 we show A has increasing principal minors if and only if A−1 exists and its diagonal entries are less or equal to 1.
Nonnegative matrices with prescribed elementary divisors.
Nonnegativity of Schur complements of nonnegative idempotent matrices.
Nonnegativity preservation under singular values perturbation.
Nonsingularity and -matrices.
New proofs of two previously published theorems relating nonsingularity of interval matrices to -matrices are given.
Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding
For a real square matrix and an integer , let denote the matrix formed from by rounding off all its coefficients to decimal places. The main problem handled in this paper is the following: assuming that has some property, under what additional condition(s) can we be sure that the original matrix possesses the same property? Three properties are investigated: nonsingularity, positive definiteness, and positive invertibility. In all three cases it is shown that there exists a real number...
Norm estimates for the inverses of matrices of monotone type and totally positive matrices.
Normalizers of Modular Groups.
Norms in Quadratic Fields and Their Relations to Non Commuting 2x2 Matrices I.
Note on some greatest common divisor matrices
Some quadratic forms related to "greatest common divisor matrices" are represented in terms of L²-norms of rather simple functions. Our formula is especially useful when the size of the matrix grows, and we will study the asymptotic behaviour of the smallest and largest eigenvalues. Indeed, a sharp bound in terms of the zeta function is obtained. Our leading example is a hybrid between Hilbert's matrix and Smith's matrix.
Note on strongly nil clean elements in rings
Let be an associative unital ring and let be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.
Note on the core matrix partial ordering
Complementing the work of Baksalary and Trenkler [2], we announce some results characterizing the core matrix partial ordering.
Notes on linear combinations of two tripotent, idempotent and involutive matrices that commute.
Notes on power LCM matrices
Notes on the divisibility of GCD and LCM matrices.
Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric -stable processes.
Numerical Solution of Linear Equations with Toeplitz and Vector Toeplitz Matrices.