A Linear Algebra Proof that the Inverse of a Strictly UltrametricMatrix is a Strictly Diagonally Dominant Stieltjes Matrix

  • Authors:

  • Reinhard Nabben;Richard S. Varga

  • Affiliations:

  • -;-

  • Venue:
  • SIAM Journal on Matrix Analysis and Applications
  • Year:
  • 1994

Quantified Score

Hi-index 0.00

Visualization

Abstract

It is well known that every $n \times n$ Stieltjes matrix has an inverse that is an $n \times n$ nonsingular symmetric matrix with nonnegative entries, and it is also easily seen that the converse of this statement fails in general to be true for $n 2$. In the preceding paper by Martinez, Michon, and San Martin [SIAM J. Matrix Anal. Appl., 15 (1994), pp. 98--106], such a converse result is in fact shown to be true for the new class of strictly ultrametric matrices. A simpler proof of this basic result is given here, using more familiar tools from linear algebra.