Natural group actions on tensor products of three real vector spaces with finitely many orbits.
Natural projectors in tensor spaces.
N-Dimensional Binary Vector Spaces
The binary set {0, 1} together with modulo-2 addition and multiplication is called a binary field, which is denoted by F2. The binary field F2 is defined in [1]. A vector space over F2 is called a binary vector space. The set of all binary vectors of length n forms an n-dimensional vector space Vn over F2. Binary fields and n-dimensional binary vector spaces play an important role in practical computer science, for example, coding theory [15] and cryptology. In cryptology, binary fields and n-dimensional...
Near threshold graphs.
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.
Negative powers and the spectrum of matrices
Nested matrices and inverse -matrices
Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the - and -factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse -matrices with symmetric, irreducible, tridiagonal inverses.
Netted matrices.
New bounds for the minimum eigenvalue of 𝓜-tensors
A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal. Appl., 2014, 2014, 114) and Zhao and Sang (J. Inequal. Appl., 2016, 2016, 268). Finally, two numerical examples are given to verify the theoretical results.
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 criteria for H-tensors and an application
Some new criteria for identifying H-tensors are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are given. Advantages of results obtained are illustrated by numerical examples.
New estimates for the solution of the Lyapunov matrix differential equation.
New families of integer matrices whose leading principal minors form some well-known sequences.
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 light on the theorem of Perron.
We prove that the principal eigenvector of a positive matrix represents the relative dominance of its rows or ranking of alternatives in a decision represented by the rows of a pairwise comparison matrix.
New limit theorems related to free multiplicative convolution
Let ⊞, ⊠, and ⊎ be the free additive, free multiplicative, and boolean additive convolutions, respectively. For a probability measure μ on [0,∞) with finite second moment, we find a scaling limit of as N goes to infinity. The -transform of its limit distribution can be represented by Lambert’s W-function. From this, we deduce that the limiting distribution is freely infinitely divisible, like the lognormal distribution in the classical case. We also show a similar limit theorem by replacing free...
New lower solution bounds for the continuous algebraic Riccati equation.