Shifting nth root algorithm not useful for computing roots with a computer, as it is always outperformed by much simpler binary search, and has the same memory complexity. 1. 0 1 1 0 1 1. 7 3 2 0 5 1. 7 0 9 9 7 1. 6 2 6 5 7 Shifting nth root algorithm The shifting "n"th root algorithm is an algorithm for extracting the "n"th root of a positive real number which proceeds iteratively by shifting in "n" digits of the radicand, starting with the most significant, and produces one digit of the root on each iteration, in a manner similar
Square root of a 2 by 2 matrix use the simplified formula where "a" = ±√"A" and "d" = ±√"D"; which, for the various sign choices, gives four, two, or one distinct matrices, if none of, only one of, or both "A" and "D" are zero, respectively. Because it has duplicate eigenvalues, the 2×2 identity matrix formula_10 has infinitely many symmetric rational square roots given by where is any Pythagorean triple—that is, any set of positive integers such that formula_12 In addition, any non-integer, irrational, or complex values of "r, s, t" satisfying formula_13 give square root matrices. The identity matrix also has infinitely many non-symmetric square roots.