Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a reality structure on a complex vector space V is a decomposition of V into two real subspaces, called the real and imaginary parts of V: V = V_mathbb{R} oplus i V_mathbb{R}. Here VR is a real subspace of V, i.e. a subspace of V considered as a vector space over the real numbers. If V has complex dimension n (real dimension 2n), then VR must have real dimension n. The standard reality structure on the vector space mathbb{C}^n is the decomposition mathbb{C}^n = mathbb{R}^n oplus i,mathbb{R}^n.

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