Shrinath Hadimani

activity

20222026

collaborators

9 papers

math.CO2026

Singular difference graphs of vector spaces of square matrices

Shrinath Hadimani

The singular difference graph, denoted by $Γ$ , of the vector space of square matrices over a field is a graph whose vertex set is the set of all elements of the vector space, where…

math.GM2026

Vieta-Type Formulas for Matrix Polynomials

Shrinath Hadimani

The classical Vieta formulas relate the coefficients of a complex scalar polynomial to the elementary symmetric polynomials of its roots. In this paper, we establish analogous spec…

math.SP2024

Stability of quaternion matrix polynomials

Pallavi Basavaraju, Shrinath Hadimani, Sachindranath Jayaraman

A right quaternion matrix polynomial is an expression of the form $P (λ) = i = 0 \sum m A_{i} λ^{i}$ , where $A_{i}$ 's are $n \times n$ quaternion matrices with $A_{m} \neq = 0$ .…

math.SP2024

On coneigenvalues of quaternion matrices: location and perturbation

Pallavi Basavaraju, Shrinath Hadimani, Sachindranath Jayaraman

We derive some localization and perturbation results for coneigenvalues of quaternion matrices. In localization results, we derive Geršgorin type theorems for right and left coneig…

math.SP2023

Bounds on the moduli of eigenvalues of rational matrices

Pallavi Basavaraju, Shrinath Hadimani, Sachindranath Jayaraman

A rational matrix is a matrix-valued function $R (λ) : C \to M_{p}$ such that $R (λ) = [r_{ij} (λ)]_{p \times p}$ , where $r_{ij} (λ)$ are scala…

math.SP2023

Eigenvalue location of certain matrix polynomials

Pallavi B, Shrinath Hadimani, Sachindranath Jayaraman

It is known that a matrix polynomial with unitary matrix coefficients has its eigenvalues in the annular region $\frac{1}{2} < ∣ λ ∣ < 2$ . We prove in this short note that under cert…

math.SP2023

The Hoffman-Wielandt inequality for quaternion matrices and quaternion matrix polynomials

Pallavi Basavaraju, Shrinath Hadimani, Sachindranath Jayaraman

The purpose of this paper is to derive the Hoffman-Wielandt inequality and its generalization for quaternion matrices. Diagonalizability of the block companion matrix of certain qu…

math.SP2023

Spectral bounds for certain special type of rational matrices

Pallavi Basavaraju, Shrinath Hadimani, Sachindranath Jayaraman

The aim of this manuscript is to derive bounds on the moduli of eigenvalues of special type of rational matrices of the form $T(λ) = \displaystyle -B_0 +Iλ+\frac{B_1}{λ-α_1}+ \dots…

math.SP2022

Hoffman-Wielandt type inequality for block companion matrices of certain matrix polynomials

Pallavi . B, Shrinath Hadimani, Sachindranath Jayaraman

Matrix polynomials with unitary/doubly stochastic coefficients form the subject matter of this manuscript. We prove that if $P (λ)$ is a quadratic matrix polynomial whose coefficien…