64 (number) it is possible to find sequences of 64 consecutive integers such that each inner member shares a factor with either the first or the last member, 64 is an Erdős–Woods number. In base 10, no integer added up to its own digits yields 64, hence it is a self number. 64 is a superperfect number—a number such that σ(σ("n")) = 2"n". 64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑ 3,… Sixty-four is: 64 (number) 64 (sixty-four) is the natural number following 63 and preceding 65. Sixty-four is the square of 8, the cube
Square root of a matrix a "positive-semidefinite matrix" has precisely one positive-semidefinite square root, which can be called its "principal square root". While the square root of a nonnegative integer is either again an integer or an irrational number, in contrast an "integer matrix" can have a square root whose entries are rational, yet not integer. For example, the matrix formula_8 has the non-integer square root formula_9 as well as the integer square root matrix formula_10. The 2×2 identity matrix is another example. A 2×2 matrix with two distinct nonzero eigenvalues has four square roots. More generally, an matrix with "distinct nonzero eigenvalues" has 2