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.
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 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 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 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 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 scaling of Itzykson–Zuber integrals
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.
Newton iteration for the closest normal matrix of order two.
Nilpotent matrices and spectrally arbitrary sign patterns.
Noncirculant Toeplitz matrices all of whose powers are Toeplitz
Let , and be fixed complex numbers. Let be the Toeplitz matrix all of whose entries above the diagonal are , all of whose entries below the diagonal are , and all of whose entries on the diagonal are . For , each principal minor of has the same value. We find explicit and recursive formulae for the principal minors and the characteristic polynomial of . We also show that all complex polynomials in are Toeplitz matrices. In particular, the inverse of is a Toeplitz matrix when...
Non-colliding random walks, tandem queues, and discrete orthogonal polynomial ensembles.
Non-commutative matrix integrals and representation varieties of surface groups in a finite group
A new formula is established for the asymptotic expansion of a matrix integral with values in a finite-dimensional von Neumann algebra in terms of graphs on surfaces which are orientable or non-orientable.
Non-existence of full ray nonsingular matrices.
Nonexistence results for Hadamard-like matrices.