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An analytical approach to Cayley-Hamilton theorem

Luiz C. Martins (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Cayley-Hamilton theorem is proved by an analytical approach by recalling certain interesting properties of density. In this process, the classical expressions of the principal invariants follow immediately from the proposed proof's scheme.

An equivalent matrix pencilfor bivariate polynomial matrices

Mohamed Boudellioua (2006)

International Journal of Applied Mathematics and Computer Science

In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.

Block diagonalization

Jaromír J. Koliha (2001)

Mathematica Bohemica

We study block diagonalization of matrices induced by resolutions of the unit matrix into the sum of idempotent matrices. We show that the block diagonal matrices have disjoint spectra if and only if each idempotent matrix in the inducing resolution double commutes with the given matrix. Applications include a new characterization of an eigenprojection and of the Drazin inverse of a given matrix.

Companion matrices and their relations to Toeplitz and Hankel matrices

Yousong Luo, Robin Hill (2015)

Special Matrices

In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices, preserving...

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