nLab
real part

Contents

Definition

Given a star-algebra (A,*)(A ,\ast) in characteristic zero, then for aAa\in A any element

  • its real part is Re(a)12(a+a *)Re(a) \coloneqq \frac{1}{2}(a + a^\ast);

  • its imaginary part is Im(a)12(aa *)Im(a) \coloneqq \frac{1}{2}(a - a^\ast).

Examples

Standard situations where real and imaginary parts are considered include the real normed division algebra

Created on March 17, 2015 at 11:28:04. See the history of this page for a list of all contributions to it.