In this paper, we consider a g-circulant matrixA 1(T), whose the first row entries are generalized Tribonacci numbers T(a)i. We give an explicit formula of spectral norm matrix. When g = 1, also present upper and lower bounds for spread 1-circulant matrix A1(T).

In this work, we are interested in non-trivial upper bounds on the spectral norm of binary matrices M from {−1, 1} . It is known that the distributed Boolean function represented by M is hard to compute in various restricted models of computation if the spectral norm is bounded from above by N, where ε > 0 denotes a fixed constant. For instance, the size of a two-layer threshold circuit (with p...

A novel quantitative structure-activity (property) relationship model, namely Spectral-SAR, is presented in an exclusive algebraic way replacing the old-fashioned multi-regression one. The actual S-SAR method interprets structural descriptors as vectors in a generic data space that is further mapped into a full orthogonal space by means of the Gram-Schmidt algorithm. Then, by coordinated transf...

In this work, we are interested in non-trivial upper bounds on the spectral norm of binary matrices M from {−1, 1}N×N . It is known that the distributed Boolean function represented by M is hard to compute in various restricted models of computation if the spectral norm is bounded from above by N1−ε, where ε > 0 denotes a fixed constant. For instance, the size of a two-layer threshold circuit (...

A 0-1 matrix where in each column the 1s occur consecutively is said to have the consecutive ones property. This property and its approximations are important in a variety of applications, e.g., in DNA analysis and paleontology. Checking whether the matrix rows can be permuted so that this property holds can be done in polynomial time. However, an exact solution rarely exists in applications. T...

In this work, the gap between operator norm and spectral radius for square of antidiagonal block matrices in direct sum Banach spaces has been investigated, also numerical same Hilbert studied.

This article is a survey of the results on asymptotic behavior small ball probabilities in $L_2$-norm. Recent progress this field mainly based methods spectral theory differential and integral operators.