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Catalogue Information
Field name	Details
Dewey Class	512
Title	Linear Algebra ([EBook]) / by W. H. Greub.
Author	Greub, Werner Hildbert , 1925-
Other name(s)	SpringerLink (Online service)
Edition statement	Third Edition.
Publication	Berlin, Heidelberg : Springer , 1967.
Physical Details	: online resource.
Series	Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 0072-7830 ; ; 97
ISBN	9783662006726
Summary Note	The major change between the second and third edition is the separation of linear and multilinear algebra into two different volumes as well as the incorporation of a great deal of new material. However, the essential character of the book remains the same; in other words, the entire presentation continues to be based on an axiomatic treatment of vector spaces. In this first volume the restriction to finite dimensional vector spaces has been eliminated except for those results which do not hold in the infinite dimensional case. The restriction of the coefficient field to the real and complex numbers has also been removed and except for chapters VII to XI, § 5 of chapter I and § 8, chapter IV we allow any coefficient field of characteristic zero. In fact, many of the theorems are valid for modules over a commutative ring. Finally, a large number of problems of different degree of difficulty has been added. Chapter I deals with the general properties of a vector space. The topology of a real vector space of finite dimension is axiomatically characterized in an additional paragraph.:
Contents note	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. Cofactors -- § 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 -- 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 the plane and of 3-space -- § 7. Differentiable 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 the orthogonal group -- § 6. Application to Lorentz-transformations -- XII. Polynomial algebra -- § 1. Basic properties -- § 2. Ideals and divisibility -- § 3. Products of relatively prime polynomials -- § 4. Factor algebras -- § 5. The structure of factor algebras -- XIII. Theory of a linear transformation -- § 1. Polynomials in a linear transformation -- § 2. Generalized eigenspaces -- § 3. Cyclic spaces and irreducible spaces -- § 4. Application of cyclic spaces -- § 5. Nilpotent and semisimple transformations -- § 6. Applications to inner product spaces.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-00672-6
Links to Related Works	Subject References: Algebra . Mathematics . Authors: Greub, Werner Hildbert 1925- . Greub, Werner Hildbert, 1925- . Corporate Authors: SpringerLink (Online service) . Series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete . Classification: 512 .

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Linear Algebra

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