1IntroductionLetA∈Cn×n,B∈Cn×n.WesayBisasquarerootofAifA=B×Bi.e.A=B2.Itiswell-knownthatanysymmetricpositivedefinitematrixexistsoneandonlyonesquarerootwhichisasymmetricpositivedefinitematrix,too（e.g.see[5]）.Higham[4]studiedcarefullytherelationofarealnonsingularmatrixbetweenitsrealsquarerootsanditseigenvalues.AlefeldandSchneider[1]pointedoutthatforanynonsingularM-ma-trixthereisoneandonlyoneM-matrixasitssquareroot.Inthispaper,westudyona
