Schaum's outline of theory and problems of linear algebra.

By seymour lipschutz.

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Schaum's outline of theory and problems of linear algebra. by Seymour Lipschutz

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Schaum's Outline of Linear Algebra, Sixth Edition

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  • Copyright Page
  • List of Symbols
  • CHAPTER 1 Vectors in Rn and Cn, Spatial Vectors
  • CHAPTER 2 Algebra of Matrices
  • CHAPTER 3 Systems of Linear Equations
  • CHAPTER 4 Vector Spaces
  • CHAPTER 5 Linear Mappings
  • CHAPTER 6 Linear Mappings and Matrices
  • CHAPTER 7 Inner Product Spaces, Orthogonality
  • CHAPTER 8 Determinants
  • CHAPTER 9 Diagonalization: Eigenvalues and Eigenvectors
  • CHAPTER 10 Canonical Forms
  • CHAPTER 11 Linear Functionals and the Dual Space
  • CHAPTER 12 Bilinear, Quadratic, and Hermitian Forms
  • CHAPTER 13 Linear Operators on Inner Product Spaces
  • APPENDIX A Multilinear Products
  • APPENDIX B Algebraic Structures
  • APPENDIX C Polynomials over a Field
  • APPENDIX D Odds and Ends

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SCHAUM'S OUTLINE OF Schaum's Outline Series 3000 SOLVED PROBLEMS IN Calculus

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1 - Pure Mathematics For Advanced Level 2nd Edition

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This is a textbook of pure mathematics written to meet the needs of the student studying for the General Certificate of Education at Advanced Level. The book assumes a knowledge of mathematics up to Ordinary Level and covers all the pure mathematics necessary for the Advanced Level examination in mathematics (A26), of the Northern Universities Joint Matriculation Board, together with the great majority of the work required for the Advanced Level examinations of the Southern Universities Joint Board, the Welsh Joint Committee and London University. The teaching method adopted is for the most part that suggested by the various reports of the Mathematical Association. The emphasis throughout has been on technique, although we have tried to indicate where a particular result needs more rigorous justification than is given in this book. In this way, we hope that all students can progress quickly in the understanding and application of these techniques without the hindrance of having to justify everything they do. This latter step comes at a later stage in their mathematical development. For convenience, the book has been prepared in the order algebra (Chapters 1-5), trigonometry (Chapters 6-8), calculus (Chapters 9-16), and co-ordinate geometry (Chapters 17-20), but this is not to imply that the chapters should be read in this order. For the student at school, this will be decided by the teacher; for the student working alone, we would recommend an advance on a broad front through Chapters 1, 3, 6, 9, 10, 12 (the first two sections), 13, 17, 18. This lays the foundations for all the main topics and this broad advance can then be maintained. We would suggest that each of Chapters 7, 11, 14, 15, 16 and 20 be read in at least two stages. Not only will this make for easier digestion of the many ideas and techniques discussed in these chapters, but will also provide for constant revision and extension of this material. The book includes over 350 worked examples and about 1800 examples for the student to solve. The worked examples indicate the main applications of the ideas and techniques discussed. The exercises set at the ends of the sections within the chapters are for the most part fairly straightforward. All our readers should attempt these exercises. The exercises at the ends of the chapters are a 'mixed bag'. Some are of a routine type, others are more testing; many are from past papers set by the various examining boards. Finally, there are some (indicated with an asterisk) which are of a more difficult

Saeed Bahatab

In exercises requiring estimations or approximations, your answers may vary slightly from the answers given here. 1. (a) The point (−1, −2) is on the graph of f , so f (−1) = −2. (b) When x = 2, y is about 2.8, so f (2) ≈ 2.8. (c) f (x) = 2 is equivalent to y = 2. When y = 2, we have x = −3 and x = 1. (d) Reasonable estimates for x when y = 0 are x = −2.5 and x = 0.3. (e) The domain of f consists of all x-values on the graph of f. For this function, the domain is −3 ≤ x ≤ 3, or [−3, 3].

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