Arithmetic and Matricial Calculation
Raoelina Andriambololona · Pure and Applied Mathematics Journal · 2016
We present a study on written numeration and arithmetic using matricial formalism for the writing of numeral basis and number. The underlying idea is simple, it consists to consider the numeral representation of number as a matrix representation of an intrinsic number in a basis which represents the numeral system. Then the matrix calculation and linear algebra tools are extensively utilized to simplify arithmetic operations and to remove many inconsistencies existing in arithmetic. Owing to the adopted convention, four dispositions are obtained for the writing of number components according to the disposition in row matrix or column matrix and in decreasing or increasing order. The writing in line from Left handside to the Right handsideby increasing order (called LRi) is shown to be much more logical and coherent with the addition and the multiplication rules than the usual one which starts from the left handside to the right handside by decreasing order (LRd). In the LRi disposition, rules for the addition and multiplication of integers number are derived.