Linear Algebra, 4th

Greub, Werner Hildbert

ISBN 10: 0387901108 / ISBN 13: 9780387901107

Editore: Springer, 1975

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***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. Sewn binding. Cloth over boards. 493 p. Contains: Illustrations. Lecture Notes in Chemistry, 23. Audience: General/trade.

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Dati bibliografici

• Titolo: Linear Algebra, 4th
• Editore: Springer
• Data di pubblicazione: 1975
• Lingua: Inglese
• ISBN 10: 0387901108
• ISBN 13: 9780387901107
• Rilegatura: Trade paperback
• Edizione: 4th ed. INTERNATIONAL EDITION
• Condizione: New in new dust jacket.

Descrizione articolo

Riassunto

This textbook gives a detailed and comprehensive presentation of the linear algebra based on axiomatic treatment of linear spaces. The author maintains a good balance between modern algebraic interests and traditional linear algebra. Several chapters have been substantially rewritten for clarity of exposition, although their basic content is unchanged. A considerable number of exer- cises covering new material has also been added.

Contenuti

0. Prerequisites.- I. Vector spaces.- § 1. Vector spaces.- § 2. Linear mappings.- § 3. Subspaces and factor spaces.- § 4. Dimension.- § 5. The topology of a real finite dimensional vector space.- II. Linear mappings.- § 1. Basic properties.- § 2. Operations with linear mappings.- § 3. Linear isomorphisms.- § 4. Direct sum of vector spaces.- § 5. Dual vector spaces.- § 6. Finite dimensional vector spaces.- III. Matrices.- § 1. Matrices and systems of linear equations.- § 2. Multiplication of matrices.- § 3. Basis transformation.- § 4. Elementary transformations.- IV. Determinants.- § 1. Determinant functions.- § 2. The determinant of a linear transformation.- § 3. The determinant of a matrix.- § 4. Dual determinant functions.- § 5. The adjoint matrix.- § 6. The characteristic polynomial.- § 7. The trace.- § 8. Oriented vector spaces.- V. Algebras.- § 1. Basic properties.- § 2. Ideals.- § 3. Change of coefficient field of a vector space.- VI. Gradations and homology.- § 1. G-graded vector spaces.- § 2. G-graded algebras.- § 3. Differential spaces and differential algebras.- VII. Inner product spaces.- § 1. The inner product.- § 2. Orthonormal bases.- § 3. Normed determinant functions.- § 4. Duality in an inner product space.- § 5. Normed vector spaces.- § 6. The algebra of quaternions.- VIII. Linear mappings of inner product spaces.- § 1. The adjoint mapping.- § 2. Selfadjoint mappings.- § 3. Orthogonal projections.- § 4. Skew mappings.- § 5. Isometric mappings.- § 6. Rotations of Euclidean spaces of dimension 2, 3 and 4.- § 7. Differentiate families of linear automorphisms.- IX. Symmetric bilinear functions.- § 1. Bilinear and quadratic functions.- § 2. The decomposition of E.- § 3. Pairs of symmetric bilinear functions.- § 4. Pseudo-Euclidean spaces.- § 5. Linear mappings of Pseudo-Euclidean spaces.- X. Quadrics.- § 1. Affine spaces.- § 2. Quadrics in the affine space.- § 3. Affine equivalence of quadrics.- § 4. Quadrics in the Euclidean space.- XI. Unitary spaces.- § 1. Hermitian functions.- § 2. Unitary spaces.- § 3. Linear mappings of unitary spaces.- § 4. Unitary mappings of the complex plane.- § 5. Application to Lorentz-transformations.- XII. Polynomial algebra.- § 1. Basic properties.- § 2. Ideals and divisibility.- § 3. Factor algebras.- § 4. The structure of factor algebras.- XIII. Theory of a linear transformation.- § 1. Polynomials in a linear transformation.- § 2. Generalized eigenspaces.- § 3. Cyclic spaces.- § 4. Irreducible spaces.- § 5. Application of cyclic spaces.- § 6. Nilpotent and semisimple transformations.- § 7. Applications to inner product spaces.