Linear Algebra: 23 (Graduate Texts in Mathematics, 23)

Greub, Werner H.

ISBN 10: 0387901108 / ISBN 13: 9780387901107

Editore: Springer, 1975

Riguardo questo articolo

The book has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains undamaged.

Codice articolo GOR014275035

Dati bibliografici

• Titolo: Linear Algebra: 23 (Graduate Texts in Mathematics, 23)
• Editore: Springer
• Data di pubblicazione: 1975
• Lingua: Inglese
• ISBN 10: 0387901108
• ISBN 13: 9780387901107
• Rilegatura: Hardback
• Edizione: quarta edizione
• Condizione: Very Good
• Peso: 812 grammi

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.