The trace invariant and matrix inversion

A stable iteration to the matrix inversion

The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. ...

Möbius inversion formula for the trace group

A trace group (monoid) is the quotient of a free group (monoid) by relations of commutation between some pairs of generators. We prove an analog for the trace group of the Möbius inversion formula for the trace monoid (Cartier and Foata, 1969). c © 200? Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Une formule d’inversion de Möbius pour le groupe de traces Résumé. Un gr...

On the Inversion Invariance of Invariant Means

An invariant mean on a group G is a normalized, positive, translation invariant linear functional defined on the space of all bounded complex valued functions on G. Some groups possess an invariant mean (or are said to be amenable), while others do not. In particular, all abelian groups are amenable [2, §17.5]. An invariant mean on a group need not be inversion invariant. It is quite easy to sh...

The Invariant Trace Formula . 11 . Global Theory

The purpose of this article is to prove an explicit invariant trace formula. In the preceding paper [l(j)] , we studied two families of invariant distributions. Now we shall exhibit these distributions as terms on the two sides of the invariant trace formula. We refer the reader to the introduction of [1 (j)], which contains a general discussion of the problem. In this introduction, we shall de...

The Invariant Trace Formula. I. Local Theory