Square root any nonnegative number, then the principal square root of −"x" is The right side (as well as its negative) is indeed a square root of −"x", since For every non-zero complex number "z" there exist precisely two numbers "w" such that : the principal square root of "z" (defined below), and its negative. There are two complex numbers that square to a given arbitrary non-zero imaginary number formula_11 with real formula_12 where the two-digit pattern {3, 6} repeats over and over again in the partial denominators. Since , the above is also identical to the following generalized continued fractions: The
Square root of a 2 by 2 matrix Square root of a 2 by 2 matrix A square root of a 2×2 matrix "M" is another 2 by 2 matrix "R" such that "M" = "R", where "R" stands for the matrix product of "R" with itself. In general there can be no, two, four or even an infinitude of square root matrices. In many cases such a matrix "R" can be obtained by an explicit formula. A 2×2 matrix with two distinct nonzero eigenvalues has four square roots. A positive-definite matrix has precisely one positive-definite square root. Square roots of a matrix of any dimension come in