## I. Bundles of Matrices and the Linear Independence of Their Minors: II. Applications of Laguerre's Method to the Matrix Eigenvalue Problem |

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### Contents

BUNDLES OF MATRICES AND THE LINEAR INDEPENDENCE OF THEIR MINORS 1 Preliminary Definitions | 2 |

Classical Results | 3 |

k A We1lKnown Lemma | 6 |

15 other sections not shown

### Common terms and phrases

_do begin abs ybar accuracy ALGOL 60 ALPHA approximation arbitrary bundles basis vector bundles are strictly Burroughs 220 calculate canonical form characteristic polynomial coefficients column complex Criterion denote derivatives determinant determinantal ideals double precision eigenvalue problem eigenvectors eigsum2 elementary divisors equation evaluation EXTERNAL PROCEDURE greatest common divisors Hessenberg form Hessenberg matrix Hy end Hyman's method Iaguerre2 imaginary initial vector inner product IROOT J. H. Wilkinson Laguerre iterates Laguerre's method lanczos Lemma linearly independent subset linearly independent t-minors lower Hessenberg maximal linearly independent multiple Newton iterate non-singular non-zero Note null number of iterations obtain OUTPUT pencils polynomials of degree polynomials with real precision number principal ideal ring Proof real roots regular bundles Section set of t-minors single precision spur spur2 spurl step strictly equivalent subtract superdiagonal t-l)-minors tally Theorem Triangular tridiagonal form tridiagonal matrix tringle xbar zero