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 there is a matrix and a diagonal matrix such that . This happens if and only if has "n" eigenvectors which constitute a basis for . In this case, can be chosen to be the matrix with the "n" eigenvectors as columns, and thus a square root of is where is any square root of . Indeed, For example, the matrix formula_14 can be diagonalized as , where giving the square root When is symmetric, the diagonalizing matrix can be made an orthogonal matrix by suitably choosing the eigenvectors (see spectral theorem). Then the inverse of is simply the transpose,