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 the state error covariance matrix is required for the unscented transform which is the statistical linearization method used. A comparison between different matrix square root calculation methods within a UKF application of GPS/INS sensor fusion was presented, which indicated that the Cholesky decomposition method was best suited for UKF applications. Square root of a matrix In mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. Matrix is said to be a square root of if the matrix product is equal to . In general, a matrix can have several square roots. For