36 (number) 36 (number) 36 (thirty-six) is the natural number following 35 and preceding 37. 36 is both the square of six and a triangular number, making it a square triangular number. It is the smallest square triangular number other than one, and it is also the only triangular number other than one whose square root is also a triangular number. It is also a circular number- a square number that ends with the same integer by itself (6×6=36). It is the smallest number "n" with exactly eight solutions to the equation φ("x") = "n". Being the smallest number with exactly nine
Square root of a matrix is an "n" × "n" complex matrix "ρ" that is positive semidefinite with trace 1. If "ρ" can be expressed as where formula_36 and ∑ "p" = 1, the set is said to be an ensemble that describes the mixed state "ρ". Notice {"v"} is not required to be orthogonal. Different ensembles describing the state "ρ" are related by unitary operators, via the square roots of "ρ". For instance, suppose The trace 1 condition means Let and "v" be the normalized "a". We see that gives the mixed state "ρ". In the Unscented Kalman Filter (UKF), the square root of