 
Summary: On Square Roots of MMatrices
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 Mmatrix which is a square
root of an Mmatrix 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 Mmatrix.
1. INTRODUCTION
Following Ostrowski [3], a real n by n matrix A=(ai;) is called an
Mmatrix 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 Mmatrix; otherwise, a singular Mmatrix.
In this paper we discuss the existence and uniqueness of an Mmatrix
which is a solution of the equation
