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Summary: On Square Roots of M-Matrices
G. Alefeld* and N. Schneider
FB 3 / Mathematik
Technische Universität Berlin
Strasse des 17. Juni 135
1()()()Berlin 12, Gernwny
Submitted by Hans Schneider
ABSTRACT
The question of the existence and uniqueness of an M-matrix which is a square
root of an M-matrix is discussed. The results are then used to derive some new
necessary and sufficient conditions for a real matrix with nonpositive off diagonal
elements to be an M-matrix.
1. INTRODUCTION
Following Ostrowski [3], a real n by n matrix A=(ai;) is called an
M-matrix if it can be written in the fonn
A=sI- B, s>O, B~O, p(B)~s. (1)
Here p denotes the spectral radius and I is the writ matrix. If p(B)
is called a rwnsingular M-matrix; otherwise, a singular M-matrix.
In this paper we discuss the existence and uniqueness of an M-matrix
which is a solution of the equation
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