Eigenvectors and minimal bases for some families of Fiedler-like linearizations Articles uri icon

publication date

  • January 2014

start page

  • 39

end page

  • 62

issue

  • 1

volume

  • 62

International Standard Serial Number (ISSN)

  • 0308-1087

Electronic International Standard Serial Number (EISSN)

  • 1563-5139

abstract

  • In this paper, we obtain formulas for the left and right eigenvectors and minimal bases of some families of Fiedler-like linearizations of square matrix polynomials. In particular, for the families of Fiedler pencils, generalized Fiedler pencils and Fiedler pencils with repetition. These formulas allow us to relate the eigenvectors and minimal bases of the linearizations with the ones of the polynomial. Since the eigenvectors appear in the standard formula of the condition number of eigenvalues of matrix polynomials, our results may be used to compare the condition numbers of eigenvalues of the linearizations within these families and the corresponding condition number of the polynomial eigenvalue problem.

keywords

  • polynomial eigenvalue problem; fiedler pencils; matrix polynomials; linearizations; eigenvector; minimal bases; symmetric matrix polynomials; matrix polynominls; backward error; linear-systems; vector-spaces; eigenproblems