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Linear algebra / by Juan Jorge Schäffer (Carnegie Mellon University, USA).

By: Schäffer, Juan JorgeMaterial type: TextTextPublisher: New Jersey : World Scientific, 2014Description: 1 online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9789814623506; 9814623504Subject(s): Algebras, Linear | Algebra | MATHEMATICS -- Algebra -- Intermediate | Algebra | Algebras, LinearGenre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Linear algebraDDC classification: 512/.5 LOC classification: QA184.2 | .S31 2014ebOnline resources: Click here to access online
Contents:
PREFACE; CONTENTS; Chapter 1. LINEAR SPACES AND LINEAR MAPPINGS; 11. Linear spaces; 12. Linear mappings; 13. Subspaces; 14. Linear partitions; 15. Supplements; Chapter 2. PROPERTIES OF LINEAR MAPPINGS; 21. Linear invertibility; 22. Cancellability and factorization; Chapter 3. LINEAR PRODUCTS AND COPRODUCTS; 31. Linear products; 32. Linear coproducts; 33. Decompositions; Chapter 4. FAMILIES IN LINEAR SPACES; 41. Linear combination; 42. Linear independence; 43. Linear independence, spanning, bases; Chapter 5. FINITE DIMENSION; 51. Matrices; 52. Finite-dimensional spaces.
53. Finite dimension and linear mappings54. Finite- and infinite-dimensional spaces; Chapter 6. DUALITY; 61. Dual spaces and transposes; 62. Annihilators; 63. Higher-order dual spaces and transposes; 64. Biorthogonal families; Chapter 7. DUALITY AND FINITE DIMENSION; 71. Duality for finite-dimensional spaces; 72. Dual bases and matrices; 73. The trace form; 74. The canonical identifications; INDEXES; Index of terms; Index of symbols.
Summary: In the spirit of the author's Basic Language of Mathematics, this companion volume is a careful exposition of the concepts and processes of Linear Algebra. It stresses cautious and clear explanations, avoiding reliance on co-ordinates as much as possible, and with special, but not exclusive, attention to the finite-dimensional situation. It is intended to also serve as a conceptual and technical background for use in geometry and analysis as well as other applications. Contents: Linear Spaces and Linear Mappings; Properties of Linear Mappings; Linear Products and Coproducts; Families in Linea.
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Includes indexes.

Includes bibliographical references and indexes.

Print version record.

PREFACE; CONTENTS; Chapter 1. LINEAR SPACES AND LINEAR MAPPINGS; 11. Linear spaces; 12. Linear mappings; 13. Subspaces; 14. Linear partitions; 15. Supplements; Chapter 2. PROPERTIES OF LINEAR MAPPINGS; 21. Linear invertibility; 22. Cancellability and factorization; Chapter 3. LINEAR PRODUCTS AND COPRODUCTS; 31. Linear products; 32. Linear coproducts; 33. Decompositions; Chapter 4. FAMILIES IN LINEAR SPACES; 41. Linear combination; 42. Linear independence; 43. Linear independence, spanning, bases; Chapter 5. FINITE DIMENSION; 51. Matrices; 52. Finite-dimensional spaces.

53. Finite dimension and linear mappings54. Finite- and infinite-dimensional spaces; Chapter 6. DUALITY; 61. Dual spaces and transposes; 62. Annihilators; 63. Higher-order dual spaces and transposes; 64. Biorthogonal families; Chapter 7. DUALITY AND FINITE DIMENSION; 71. Duality for finite-dimensional spaces; 72. Dual bases and matrices; 73. The trace form; 74. The canonical identifications; INDEXES; Index of terms; Index of symbols.

In the spirit of the author's Basic Language of Mathematics, this companion volume is a careful exposition of the concepts and processes of Linear Algebra. It stresses cautious and clear explanations, avoiding reliance on co-ordinates as much as possible, and with special, but not exclusive, attention to the finite-dimensional situation. It is intended to also serve as a conceptual and technical background for use in geometry and analysis as well as other applications. Contents: Linear Spaces and Linear Mappings; Properties of Linear Mappings; Linear Products and Coproducts; Families in Linea.

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