Square and Compasses Square and Compasses The Square and Compasses (or, more correctly, a square and a set of compasses joined together) is the single most identifiable symbol of Freemasonry. Both the square and compasses are architect's tools and are used in Masonic ritual as emblems to teach symbolic lessons. Some Lodges and rituals explain these symbols as lessons in conduct: for example, Duncan's Masonic Monitor of 1866 explains them as: "The square, to square our actions; The compasses, to circumscribe and keep us within bounds with all mankind". However, as Freemasonry is non-dogmatic, there is no general interpretation for these symbols (or
Square root of a matrix a "positive-semidefinite matrix" has precisely one positive-semidefinite square root, which can be called its "principal square root". While the square root of a nonnegative integer is either again an integer or an irrational number, in contrast an "integer matrix" can have a square root whose entries are rational, yet not integer. For example, the matrix formula_8 has the non-integer square root formula_9 as well as the integer square root matrix formula_10. The 2×2 identity matrix is another example. A 2×2 matrix with two distinct nonzero eigenvalues has four square roots. More generally, an matrix with "distinct nonzero eigenvalues" has 2