Unit group

In Mathematical, the unit group of degree N on a body E (which is very often the body \ mathbb R of the real numbers or the body \ mathbb C of the complex numbers) is the group unit matrices N × N with coefficients in E , provided with the matric multiplication. It is noted U ( N , E ), or U ( N ) when there is no ambiguity on E . It is a Sous-groupe linear general Groupe GL ( N , E ).

U ( N , \ mathbb R) coincides with the orthogonal Groupe O ( N , \ mathbb R). This is why U ( N , \ mathbb C) is generally shortened out of U ( N ), because the distinction is not necessary.

If N =1, U (1) is isomorphous with the whole of the complex numbers of Module 1, provided with the multiplication.

U ( N ) is a real Groupe of Dregs of dimension N 2. The Algèbre of Dregs of U ( N ) is formed of the complex matrices antihermitiennes N × N .

See too

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