Appendix D Notation
| Symbol | Description | Location |
|---|---|---|
| \(\C\) | the set of complex numbers | Paragraph |
| \(\R\) | the set of real numbers | Paragraph |
| \(\Quat\) | the set of quaternions | Paragraph |
| \(\R^3_\Quat\) | the space of pure quaternions | Paragraph |
| \(U(\Quat)\) | the set of unit quaternions | Paragraph |
| \(S^1\) | unit circle in the plane | Paragraph |
| \(\extR\) | extended real numbers | Paragraph |
| \(S^2\) | unit sphere in \(\R^3\) | Paragraph |
| \(\extC\) | extended complex numbers | Paragraph |
| \([x]\) | the equivalence class of an element \(x\) | Paragraph |
| \(X/\!\!\sim\) | the set of equivalence classes for an equivalence relation \(\sim\) | Paragraph |
| \(\Perm(X)\) | permutations of a set \(X\) | Definition 2.1.1 |
| \(S_n\) | the symmetric group on \(n\) symbols | Definition 2.1.1 |
| \(R_\theta\) | rotation by angle \(\theta\) | Assemblage |
| \(F_L\) | reflection across line \(L\) | Assemblage |
| \(D_n\) | dihedral group | Definition 2.1.5 |
| \(GL(n,\R)\) | the group of \(n\times n\) invertible matrices with real entries | Definition 2.1.10 |
| \(GL(n,\C)\) | the group of \(n\times n\) invertible matrices with complex entries | Definition 2.1.10 |
| \(k^\ast\) | group of nonzero elements in a field \(k\) | Definition 2.1.11 |
| \(|G|\) | order of the group \(G\) | Definition 2.2.6 |
| \(C(a)\) | the centralizer of an element \(a\) in a group \(G\) | Exercise 2.3.4 |
| \(Z(G)\) | the center of a group | Exercise 2.3.4 |
| \(G\approx H\) | group \(G\) is isomorphic to group \(H\) | Definition 2.4.1 |
| \( H\trianglelefteq G \) | \(H\) is a normal subgroup of \(G\) | Definition 2.4.8 |
| \(\Orb(x)\) | orbit of \(x\) under a group action | Definition 2.5.1 |
| \(\Stab(x)\) | stabilizer of an element \(x\) under a group action | Definition 2.5.1 |
| \(X/G\) | set of orbits of the action of group \(G\) on set \(X\) | Proposition 2.5.4 |
| \(\Proj(V) \) | projective space | Exercise 2.5.2.4 |
| \(F \cong F'\) | figure \(F\) is congruent to figure \(F'\) | Definition 3.1.1 |