Finding the characteristic polynomial of a matrix is a fundamental task in linear algebra, with applications ranging from determining eigenvalues and eigenvectors to analyzing the stability of systems ...

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 ...

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 ...

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 ...

Abstract: In this paper, we present a new, necessary and sufficient condition for Hurwitz stability of real matrix, using qualitative (based solely on sign pattern of the matrix) reasoning. This new ...

ABSTRACT: Let A be the linear transformation on the linear space V in the field P, V λ i be the root subspace corresponding to the characteristic polynomial of the eigenvalue λ i , and W λ i be the ...