The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group
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abelian group additive algebraic association assume automorphism basis bijection called Chapter coefficients common commutative complex numbers conclude consisting contains Corollary coset cyclic define definition denote denumerable distinct divides divisor elements embedding equal equivalent Example Exercise exists expression fact factor field finite follows functions Galois group give given Hence homomorphism ideal induction infinite injective inverse irreducible polynomial isomorphism kernel leave left ideal Lemma Let f Let G lies linear map matrices means module multiplication namely non-zero normal Note obtain pairs period permutation polynomial positive integer prime number Proof properties prove quotient rational numbers real numbers relation relatively prime representative ring root satisfying sequence Show subgroup subgroup of G subset Suppose surjective Theorem uniquely determined unit element vector space verify whence write written zero