Integer matrix

Integer matrices find frequent application in combinatorics.

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.

, which has far-reaching applications in arithmetic and geometry.

, it is closely related to the modular group.

The intersection of the integer matrices with the orthogonal group is the group of signed permutation matrices.

Since the eigenvalues of a matrix are the roots of this polynomial, the eigenvalues of an integer matrix are algebraic integers.

In dimension less than 5, they can thus be expressed by radicals involving integers.