Currently displaying 1 – 3 of 3

Showing per page

Order by Relevance | Title | Year of publication

On characteristic and permanent polynomials of a matrix

Ranveer SinghR. B. Bapat — 2017

Special Matrices

There is a digraph corresponding to every square matrix over ℂ. We generate a recurrence relation using the Laplace expansion to calculate the characteristic and the permanent polynomials of a square matrix. Solving this recurrence relation, we found that the characteristic and the permanent polynomials can be calculated in terms of the characteristic and the permanent polynomials of some specific induced subdigraphs of blocks in the digraph, respectively. Interestingly, these induced subdigraphs...

The Smith normal form of product distance matrices

R. B. BapatSivaramakrishnan Sivasubramanian — 2016

Special Matrices

Let G = (V, E) be a connected graph with 2-connected blocks H1, H2, . . . , Hr. Motivated by the exponential distance matrix, Bapat and Sivasubramanian in [4] defined its product distance matrix DG and showed that det DG only depends on det DHi for 1 ≤ i ≤ r and not on the manner in which its blocks are connected. In this work, when distances are symmetric, we generalize this result to the Smith Normal Form of DG and give an explicit formula for the invariant factors of DG.

Page 1

Download Results (CSV)