## On the matrix polynomial, Lambda-matrix and block eigenvalue problems |

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### Contents

Solvents | 11 |

Properties of Matrix Polynomials | 29 |

The Block Vandermonde | 36 |

9 other sections not shown

### Common terms and phrases

Bell Telephone Laboratories Bernoulli iteration Bernoulli method Bezout's Theorem block companion matrix block eigen block eigenvalue problem block eigenvector block linearly independent block matrix block vector chain of solvents Chapter CN CN cn o cn columns common eigenvalues complete set computations considered convergence theorem Definition distinct latent roots dominant latent root dominant solvent Eh co tH Eh Eh Eh eigenvector powering exists a unique full rank fundamental matrix polynomials Gaussian elimination given Gn(X hence is_ nonsingular Jordan form lambda lambda-matrix problem lambda-vector Lancaster leading matrix coefficient left solvent Lemma locally convergent matrix polynomial M(X matrix polynomial problem monic matrix polynomial monic polynomial Newton's method nomial nonsingular matrix order mn principal vectors Proof result follows right solvents roots of M(X scalar polynomial algorithm second stage set of block set of right set of solvents solvent of M(X Theorem 5.1 Traub's scalar polynomial Vandermonde matrix