A Short Note on the Determinant of a Sylvester–Kac Type Matrix
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Carlos M. da Fonseca
Abstract
The Sylvester–Kac matrix, also known as Clement matrix, has many extensions and applications. The evaluation of determinant and spectra of many of its generalizations sometimes are hard to compute. Recently, E. Kılıç and T. Arikan proposed an extension the Sylvester–Kac matrix, where the main diagonal is a 2-periodic sequence. They found its determinant using a spectral technique. In this short note, we provide a simple proof for that result by calculating directly the determinant.
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Validation of SPH-FE Numerical Modeling of the Interaction between a High-Speed Water Jet and a PMMA Target by CEL Model and Experimental Study
- Dynamical Analysis of Fractional Order Model for Computer Virus Propagation with Kill Signals
- The Functional Variable Method to Find New Exact Solutions of the Nonlinear Evolution Equations with Dual-Power-Law Nonlinearity
- Mathematical Study of a Class of Epidemiological Models with Multiple Infectious Stages
- Brownian Motion on Cantor Sets
- Characteristics of Abundant Lumps and Interaction Solutions in the (4+1)-Dimensional Nonlinear Partial Differential Equation
- Analysis of a Non-integer Order Model for the Coinfection of HIV and HSV-2
- Bifurcation Analysis of an Electro-Statically Actuated Nano-beam Based on the Nonlocal Theory considering Centrifugal Forces
- Unsteady Self-similar Flow over an Impulsively Started Shrinking Sheet: Flow Augmentation with No Separation
-
Existence, Uniqueness and Stability of Implicit Switched Coupled Fractional Differential Equations of
- Dynamical Study of Competition Cournot-like Duopoly Games Incorporating Fractional Order Derivatives and Seasonal Influences
- A Short Note on the Determinant of a Sylvester–Kac Type Matrix
- Modeling the Impact of Rain on Population Exposed to Air Pollution
- Lump and Lump–Kink Soliton Solutions of an Extended Boiti–Leon–Manna–Pempinelli Equation
- Analysis of a Convective-Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity
- Constrained Optimal Control of A Fractionally Damped Elastic Beam
