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 finitely many terms will be non-zero and It suffices to check uniqueness for a Jordan block with λ = 1. The square constructed above has the form "S" = "I" + "L" where "L" is polynomial in "N" without constant term. Any other square root "T" with positive eigenvalues has the form "T" = "I" + "M" with nilpotent, commuting with "N" and hence "L". But then . Since "L" and commute, the matrix is nilpotent and is invertible with inverse given by a Neumann series. Hence "L" = . If is a matrix with positive eigenvalues and minimal polynomial