Integer (computer science) at least 32 bits on any computer. Programmers may also incorrectly assume that a pointer can be converted to an integer without loss of information, which may work on (some) 32-bit computers, but fail on 64-bit computers with 64-bit pointers and 32-bit integers. A "short integer" can represent a whole number that may take less storage, while having a smaller range, compared with a standard integer on the same machine. In C, it is denoted by short. It is required to be at least 16 bits, and is often smaller than a standard integer, but this is not required. A
Integer matrix not become excessively large (see condition number). Theorems from matrix theory that infer properties from determinants thus avoid the traps induced by ill conditioned ("nearly" zero determinant) real or floating point valued matrices. The inverse of an integer matrix formula_3 is again an integer matrix if and only if the determinant of formula_3 is exactly formula_5 or formula_6. Integer matrices of determinant formula_5 form the group formula_8, which has far-reaching applications in arithmetic and geometry. For formula_9, it is closely related to the modular group. The intersection of the integer matrices with the orthogonal group is the group of signed