AlgebraThis book is for the honors undergraduate or introductory graduate course. Linear algebra is tightly integrated into the text. |
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a₁ abelian group algebraic arbitrary automorphism basis bijective called Chapter coefficients column vector complex numbers Compute conjugacy classes conjugate contains Corollary cosets cyclic group defined denote Determine diagonal dihedral group dot product eigenvalues eigenvector element of G entries equation example factors field F finite group formula function Galois group group G group of order hence hermitian homomorphism identity integer invertible irreducible polynomial isomorphic kernel lattice law of composition left multiplication Lemma Let G Let H linear combination linear operator linearly independent matrix modulo nonzero normal subgroup notation orbit orthogonal permutation permutation matrix plane positive definite prime Proof Proposition Prove quadratic real numbers relation ring root rotation scalar Section solution splitting field SU₂ subgroup of G subset subspace Sylow Sylow p-subgroup symmetric group Theorem tion unitary v₁ vector space w₁ zero