Chapter 7 Partitions of Unity, Orientability, Covering Maps ~
... Either det(g) is negative or it is positive. Thus, we define an equivalence relation on bases by saying that two bases have the same orientation i↵ the determinant of the linear map sending the first basis to the second has positive determinant. An orientation of E is the choice of one of the two eq ...
... Either det(g) is negative or it is positive. Thus, we define an equivalence relation on bases by saying that two bases have the same orientation i↵ the determinant of the linear map sending the first basis to the second has positive determinant. An orientation of E is the choice of one of the two eq ...
Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power n. Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory of group characters, and the discrete Fourier transform.In field theory and ring theory the notion of root of unity also applies to any ring with a multiplicative identity element. Any algebraically closed field has exactly n nth roots of unity, if n is not divisible by the characteristic of the field.