The Algebraic Theory of Matrix Polynomials

  title={The Algebraic Theory of Matrix Polynomials},
  author={J. E. Dennis and J. Traub and R. Weber},
  journal={SIAM Journal on Numerical Analysis},
A matrix S is a solvent of the matrix polynomial $M(X) = A_0 X^m + \cdots + A_m $ if $M(S) = 0$ where $A_i ,X,S$ are square matrices. In this paper we develop the algebraic theory of matrix polynomials and solvents. We define division and interpolation, investigate the properties of block Vandermonde matrices, and define and study the existence of a complete set of solvents. We study the relation between the matrix polynomial problem and the lambda-matrix problem, which is to find a scalar… Expand
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