in 1963 when mcgraw-hill published "differential geometry" by heinrich guggenheimer of the university of minnesota, he uses the row vector convention in chapter 5, "introduction to transformation groups" (eqs. 7a,9b and 12 to 15). when h. s. m. coxeter reviewed "linear geometry" by rafael artzy, he wrote, "[artzy] is to be congratulated on his choice of the 'left-to-right' convention, which enables him to regard a point as a row matrix instead of the clumsy column that many authors prefer." j. w. p. hirschfeld used right multiplication of row vectors by matrices in his description of projectivities on the galois geometry pg(1,q).