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Linear algebra /
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
[1968]
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.