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.

Reliable data analysis is one of the hardest tasks in sciences and social sciences. Often misleading and sometimes puzzling results arise when the analysis is done without regard for the special features of the data. In this exposition, I will focus on designing new statistical tools to deal...