General Linear Group Definition Determinant Definition Connected Component Definition Möbius Formula for Euler's Totient Function Algebra Completeness of Irreducible Characters Representation Theory Functoriality of $K_1$ Algebra Polarisation Identity Linear Algebra Zariski's Lemma Algebra Alternating Groups Are Simple Group Theory Continuous Homomorphisms $\mathbb{R} \to S^1$ Representation Theory Double Dual And Double Annihilator Linear Algebra Algebra Area