Author

Kailash M. Patil

Department of Mathematics, Faculty of Technology, Dharmsinh Desai University, Nadiad, Gujarat, 387001, India

Published papers: 2
Citations: 1
Views: 569
Downloads: 234

Publications

2 papers

Open Access Research Article·pp. 639–650·Vol. 27, Issue 2-BMar 2024

Some applications of trace of powers of matrices to graph theory, algebra and combinatorics

Kailash M. Patil

Published Online: 11 Apr 2024DOI: 10.47974/JDMSC-1909

In this paper: In this paper, using Cayley Hamilton Theorem, we exhibit a combinatorial formula for Tr(An), (n ∈ ℤ, A ∈M3 (K)), over the field K(= ℝorℂ)using Tr (A), det(A) and sum of principal minors of A. Further,...

Abstract References Full Text PDF (553 KB)Views: 256Downloads: 100Citations: 0

Open Access Research Article·pp. 181–189·Vol. 27, Issue 2Mar 2024

On the combinatorial identities using the nth power of square matrix

Gopal K. Gohel, Kailash M. Patil

Published Online: 19 Mar 2024DOI: 10.47974/JIM-1808

In this paper: In this paper, we provide an independent proof for calculating the power of a matrix,whereour proof complements the theorem established by McLaughlin in 2004 [10,p-3]. Additionally, we obtain some nov...

Abstract References Full Text PDF (157 KB)Views: 313Downloads: 134Citations: 1