Nearly principal minors of -matrices
Necessary and sufficient conditions for the existence of a Hermitian positive definite solution of a type of nonlinear matrix equations.
New bounds for the minimum eigenvalue of the Fan product of two -matrices
In this paper, we mainly use the properties of the minimum eigenvalue of the Fan product of -matrices and Cauchy-Schwarz inequality, and propose some new bounds for the minimum eigenvalue of the Fan product of two -matrices. These results involve the maximum absolute value of off-diagonal entries of each row. Hence, the lower bounds for the minimum eigenvalue are easily calculated in the practical examples. In theory, a comparison is given in this paper. Finally, to illustrate our results, a simple...
New bounds for the minimum eigenvalue ofM-matrices
Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.
New iterative codes for𝓗-tensors and an application
New iterative codes for identifying 𝓗 -tensor are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given. Advantages of results obtained are illustrated by numerical examples.
New kinds of theorems on non-negative matrices
New results about semi-positive matrices
Our purpose is to present a number of new facts about the structure of semipositive matrices, involving patterns, spectra and Jordon form, sums and products, and matrix equivalence, etc. Techniques used to obtain the results may be of independent interest. Examples include: any matrix with at least two columns is a sum, and any matrix with at least two rows, a product, of semipositive matrices. Any spectrum of a real matrix with at least elements is the spectrum of a square semipositive matrix,...
New stability conditions for positive continuous-discrete 2D linear systems
New necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.
Non-existence of full ray nonsingular matrices.
Nonnegative matrices with prescribed elementary divisors.
Nonnegativity of Schur complements of nonnegative idempotent matrices.
Nonnegativity preservation under singular values perturbation.
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.
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.