Undergraduate Algebra: A First CourseDesigned for second-year mathematics students, this book offers a modern, highly systematic approach to thoroughly familiarize students with the theory of rings, fields, vector spaces, and particularly with the techniques of matrix manipulation. In keeping the needs of the learner paramount, the author provides motivation at each difficult point and integrates a wide range of exercises into each chapter. The method is both strong in its presentation of linear algebra and relevant to computer science. |
Contents
Preliminary concepts | 1 |
Rings fields and complex numbers | 31 |
Integers | 67 |
Copyright | |
21 other sections not shown
Common terms and phrases
1-element a₁ addition and multiplication belong bijective called characteristic polynomial characteristic roots characteristic vectors coefficient column commutative ring complex numbers congruence corresponding coset defined Definition denote diagonal divisor e₁ elements entries equation equivalence relation Euclidean space factors field F finite finite-dimensional hence hermitian integer integral domain invertible matrix irreducible irreducible polynomials isomorphism j)-entry linear combination linear mapping linearly independent matrix over F modulus monic natural number non-zero notation nxn matrix obtain orthogonal orthonormal basis permutations positive Proof Proposition Let r₁ rank reader real numbers ring homomorphism row-equivalent row-reduced echelon form satisfies scalar multiplication Show solution subgroup subring subsets subspace suppose surjective symmetric theorem U₁ U₂ unique unitary space v₁ v₂ vector space verify W₁ write x₁ y₁ Z₂ zero