A note on estimate of the spectral radius of symmetric matrices
A note on estimates for the spectral radius of a nonnegative matrix.
A note on estimates of diagonal elements of the inverse of diagonally dominant tridiagonal matrices.
A Note on Extreme Positive Definite Matrices.
A note on Fibonacci matrices of even degree.
A note on generalized Perron complements of -matrices.
A note on hypervector spaces
The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.
A note on indecomposability of Boolean matrices
A note on involutory automorphisms of and the use of algebraically independent numbers for the construction of diagonable matrices
A note on Kantorovich inequality for Hermite matrices.
A note on linear approximations of matrices
A note on linear discrepancy.
A note on majorization transforms and Ryser’s algorithm
The notion of a transfer (or T -transform) is central in the theory of majorization. For instance, it lies behind the characterization of majorization in terms of doubly stochastic matrices. We introduce a new type of majorization transfer called L-transforms and prove some of its properties. Moreover, we discuss how L-transforms give a new perspective on Ryser’s algorithm for constructing (0; 1)-matrices with given row and column sums.
A note on minimum rank and maximum nullity of sign patterns.
A note on Newton and Newton-like inequalities for -matrices and for Drazin inverses of -matrices.
A note on nonnegative matrices
A note on preserving the spark of a matrix
Let Mm×n(F) be the vector space of all m×n matrices over a field F. In the case where m ≥ n, char(F) ≠ 2 and F has at least five elements, we give a complete characterization of linear maps Φ: Mm×n(F) → Mm×n(F) such that spark(Φ(A)) = spark(A) for any A ∈Mm×n(F).
A note on regularity and positive definiteness of interval matrices
We present a sufficient regularity condition for interval matrices which generalizes two previously known ones. It is formulated in terms of positive definiteness of a certain point matrix, and can also be used for checking positive definiteness of interval matrices. Comparing it with Beeck’s strong regularity condition, we show by counterexamples that none of the two conditions is more general than the other one.
A note on resolving the inconsistency of one-sided max-plus linear equations
When a system of one-sided max-plus linear equations is inconsistent, its right-hand side vector may be slightly modified to reach a consistent one. It is handled in this note by minimizing the sum of absolute deviations in the right-hand side vector. It turns out that this problem may be reformulated as a mixed integer linear programming problem. Although solving such a problem requires much computational effort, it may propose a solution that just modifies few elements of the right-hand side vector,...
A Note on Sub-Multiplicative Norms.