Classification and application of triangular quark mass matrices

Any given pair of up and down quark mass matrices can be brought into the triangular form, at the same time eliminating their unphysical contents. Further, we show that every physically viable pair can always be reduced to one of ten triangular forms, which we list explicitly. When hermitian mass matrices are thus analyzed, it is found that any pattern of texture zeros translates into simple, analytic predictions for the quark mixings. Amongst possible hermitian matrices with five texture zeros, this method enables us to identify the unique pair which is favored by present data.