Results 1 to 10 of about 2,263,836 (123)

The spectral norms of geometric circulant matrices with the generalized k-Horadam numbers [PDF]

Journal of Inequalities and Applications, 2018
In this paper, we use the algebra methods, the properties of the r-circulant matrix and the geometric circulant matrix to study the upper and lower bound estimate problems for the spectral norms of a geometric circulant matrix involving the generalized k-
Baijuan Shi
doaj   +5 more sources

On the bounds for the spectral norms of geometric circulant matrices [PDF]

Journal of Inequalities and Applications, 2016
In this paper, we define a geometric circulant matrix whose entries are the generalized Fibonacci numbers and hyperharmonic Fibonacci numbers. Then we give upper and lower bounds for the spectral norms of these matrices.
Can Kızılateş, Naim Tuglu
doaj   +5 more sources

A COMPUTATION PERSPECTIVE FOR THE EIGENVALUES OF CIRCULANT MATRICES INVOLVING GEOMETRIC PROGRESSION

Jurnal Matematika UNAND, 2023
In this article, the eigenvalues and inverse of circulant matrices with entries in the first row having the form of a geometric sequence are formulated explicitly in a simple form in one theorem. The method for deriving the formulation of the determinant
SISWANDI SISWANDI, SUGI GURITMAN, NUR ALIATININGTYAS, TEDUH WULANDARI   +3 more
doaj   +3 more sources

Some results on geometric circulant matrices involving the Leonardo numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In this study, by the motivation of the papers in the literature, we construct a special geometric circulant matrix Leᵣ* whose entries are the Leonardo numbers. Then, we investigate some linear algebraic properties of these matrices.
Samet Arpacı, Fatih Yılmaz
doaj   +3 more sources

On the spectral norms of some circulant matrices with the trigonometric functions

Journal of Inequalities and Applications, 2019
In this paper, we use the properties of an r-circulant matrix and a geometric circulant matrix to study the spectral norms of the r-circulant matrix and the geometric circulant matrix involving trigonometric functions by some algebra methods.
Baijuan Shi
doaj   +1 more source

The theory and applications of complex matrix scalings

Special Matrices, 2014
We generalize the theory of positive diagonal scalings of real positive definite matrices to complex diagonal scalings of complex positive definite matrices.
Pereira Rajesh, Boneng Joanna
doaj   +1 more source

Some bounds for the spectral norms of some circulant matrices with generalized Jacobsthal–Lucas numbers

Mathematics Open
The purpose of this paper is to investigate the bounds of the spectral norms of some circulant matrices whose elements are a generalization of Jacobsthal–Lucas numbers called bi-periodic Jacobsthal–Lucas numbers by three different ways.
Sukran Uygun
doaj   +1 more source

Curvature-Corrected Rotary Position Embeddings: An Entropy-Invariant Temperature for Mitigating Numerical-Rank Collapse in Long-Context Attention

Mathematics
As large language models process ever longer contexts, the positional encoding—most commonly rotary position embeddings (RoPEs)—must remain numerically trustworthy.
Joseph Tafataona Mtetwa, Kingsley A. Ogudo, Sameerchand Pudaruth   +2 more
doaj   +1 more source

Quantum computing and preconditioners for hydrological linear systems. [PDF]

Sci Rep, 2022
Golden J, O'Malley D, Viswanathan H.
europepmc   +1 more source

Geometrization for Energy Levels of Isotropic Hyperfine Hamiltonian Block and Related Central Spin Problems for an Arbitrarily Complex Set of Spin-1/2 Nuclei. [PDF]

Int J Mol Sci, 2022
Stass DV.
europepmc   +1 more source