Abstract: As a fundamental work on coding theory, the characteristic polynomial for symmetric companion matrix of an extended field with the characteristic number 2 is investigated. A new linear ...

Abstract: Matrix calculus [2], [7] is used to derive formulas for the derivatives of the coefficients of the characteristic polynomial with respect to any matrix of physical parameters. Two of these ...

We present a conjectural formula for the principal minors and the characteristic polynomial of Gross’s regulator matrix associated to a totally odd character of a totally real field. The formula is ...

The second path matrix S(G) collects all the second paths in the graph G. Its characteristic polynomial shows some regularity in several particular graphs, such as paths, cycles, stars and complete ...

In this paper, the notion of equitable partitions (EP) is used to study the eigenvalues of Euclidean distance matrices (EDMs). In particular, EP is used to obtain the characteristic polynomials of ...

A simple formula is established that relates the trace of the resolvent with the characteristic polynomial of a matrix. This will lead to a novel and elegant proof of the recursive relations that ...