dual space Definition dimension Definition Dual Basis Theorem #414 Tensor Product of Representations Representation Theory Structural Isomorphisms of Compact Lie Groups Representation Theory Conjugacy Class Splitting Criterion Representation Theory Galois Group of Finite Field Extension Algebra Centralizer of a Cartan Subalgebra Algebra Irreducible Representations of $\operatorname{U}(2)$ Representation Theory Elementary Reduction To Canonical Form Linear Algebra Spectral Theorem For Unitary Maps Linear Algebra Algebra Area Linear Algebra Subarea