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Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the m...
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| Main Authors: | |
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| Corporate Authors: | |
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| Published: |
Academic Press,
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| Publisher Address: | New York : |
| Publication Dates: | [1968] |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/book/9781483232089 |
| Summary: |
Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand. |
| Carrier Form: | 1 online resource (x, 326 pages) |
| Bibliography: | Includes bibliographical references (pages 313-315). |
| ISBN: |
9781483265230 1483265234 9781483232089 1483232085 |
| Index Number: | QA251 |
| CLC: | O151.2 |
| Contents: |
Front Cover; Linear Algebra; Copyright Page; Preface; Table of Contents; Symbols; Chapter 1. VECTOR SPACES; 1 VECTORS; 2 DEFINITIONS OF A VECTOR SPACE; 3 SUBSPACES AND THEIR ALGEBRA; 4 VECTOR SPACES OVER ARBITRARY FIELDS; Chapter 2. FURTHER PROPERTIES OF VECTOR SPACES; 1 BASES AND DIMENSION; 2 ISOMORPHISM; 3 CALCULATION METHODS; 4 CHANGE OF BASIS; 5 GEOMETRIC ASPECTS OF VECTOR SPACES; Chapter 3. INNER-PRODUCT SPACES; 1 EUCLIDEAN SPACES; 2 ORTHONORMAL BASES; 3 DISTANCES AND NORMS; 4 ORTHOGONAL COMPLEMENTS AND ORTHOGONAL PROJECTIONS; 5 UNITARY SPACES; Chapter 4. LINEAR TRANSFORMATIONS. 1 DEFINITION OF A LINEAR TRANSFORMATION2 RANGE, NULL SPACE, RANK, AND NULLITY; 3 THE VECTOR SPACES L (V, W) AND L (V, V); 4 LINEAR FUNCTIONALS AND DUAL SPACES; 5 ANNIHILATORS; 6 ADJOINTS; 7 UNITARY AND ORTHOGONAL TRANSFORMATIONS; Chapter 5. MATRICES; 1 RANK; 2 SIMILAR LINEAR TRANSFORMATIONS AND MATRICES; 3 ELEMENTARY MATRICES; 4 TRIANGULAR MATRICES; 5 DETERMINANTS; Chapter 6. ALGEBRAIC PROPERTIES OF LINEAR TRANSFORMATIONS; 1 POLYNOMIAL RINGS; 2 MINIMAL POLYNOMIALS; 3 CHARACTERISTIC VALUES AND VECTORS; 4 DLAGONALIZATION OF SELF-ADJOINT TRANSFORMATIONS; 5 CHARACTERISTIC POLYNOMIALS. 6 TRIANGULABLE LINEAR TRANSFORMATIONSChapter 7. BILINEAR FORMS AND QUADRATIC FORMS; 1 BILINEAR FORMS; 2 QUADRATIC FORMS; 3 EXTERNAL PROPERTIES OF CHARACTERISTIC VALUES OF A SYMMETRIC MATRIX; Chapter 8. DECOMPOSITION THEOREMS FOR NORMAL TRANSFORMATIONS; 1 DIRECT SUMS AND PROJECTIONS; 2 A DECOMPOSITION THEOREM; 3 NORMAL TRANSFORMATIONS; 4 THE JORDAN NORMAL FORM; Chapter 9. SEVERAL APPLICATIONS OF LINEAR ALGEBRA; 1 LINEAR DIFFERENTIAL EQUATIONS; 2 ECONOMICS: INTERACTIONS AMONG INDUSTRIES AND CONSUMERS; 3 CHEMISTRY: ANALYSIS OF MULTICOMPONENT MIXTURES; 4 PHYSICS: COUPLED OSCILLATIONS AND NORMAL MODES5 CHEMICAL PHYSICS : THE HARMONIC OSCILLATOR; Appendix: NOTIONS OF SET THEORY; INDEX. |