This note derives an explicit formula for the numerical calculation of the square root of a matrix, when this function exists. An example is given as an illustration of the formula. The condition for the existence of the square root is also given.

This paper is interested to propose an alternative approach entitled the input-output multi-dimensional analysis. This approach is based on the interaction among four production sectors (agriculture, light industry, heavy industry and services) by “i” number of sub-sectors under the uses of...