Record Details     « New Search       Brief Record Full Record MARC Record     Bibliographic Data Control Number 335012 Date and Time of Latest Transaction 20180522074312.AM General Information 180522s |||||||||b ||00||| Cataloging Source STII-DOST Language Code eng Local Call Number Fil Q149 P5 N25 v.14 Main Entry - Personal Name Cawagas, Raoul E. Title Statement The sign matrix concept and some applications in abstract algebra and theoretical physics by Raoul E. Cawagas Physical Description 121-140 figures, illustrations Summary, Etc. This paper introduces the concept of the mxn sign matrix (or Z-matrix) Z = (zij)' over the number set F = {+1. -l}. where Zij = ±l (or simply + or -) for every i=l •.•. ,mandfor every j:::l •...• n (m. n any two positive integers). The Hadamard matrix is a special kind of nxn Z-matrix whose rows are mutually orthogonal. Given a;'1y two mxn Z-matrices Za = ([za]y) and Zb = ([zbhj)' we define their star product, Za*Zb' to be the matrix Zc = ([zcJij)' where [zchj = [zahj • [zbhj for all i=l, ... ,m, j=l, ... ,n and• is ordinary multiplication of real numbers. Under this matrix. operation. *. the set Z(mxn) of all the 2mxn possible mxn sign matrices form an abelian p-group of order 2mxn isomorphic to the Klein group of the same order. Z-matrices can be used to construct a family of division algebras of order 2r (r any positive integer) over the real numbers as well as special groups (such as the group of Dirac operators in quantum electrodynamics) and pseudogroups with important applications in pure mathematics and theoretical physics Subject Added Entry - Topical Term Science and technology   Abstract algebra   Theoretical physics   Sign matrix   Klein group   Mathematical science           Physical Location           Digital Copy Not Available          Add to Book Cart  |   Download MARC