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 matrix linear map is completely positive if and only if it is of the form where "k" ≤ "nm". Let {"E"} ⊂ C be the "n" elementary matrix units. The positive matrix is called the "Choi matrix" of Φ. The Kraus operators correspond to the, not necessarily square, square roots of "M": For any square root "B" of "M", one can obtain a family of Kraus operators "V" by undoing the Vec operation to each column "b" of "B". Thus all sets of Kraus operators are related by partial isometries. In quantum physics, a density matrix for an "n"-level quantum system