Introduction to linear algebra / Serge Lang.
Series Undergraduate texts in mathematicsEditor: New York : Springer-Verlag, c1986Edición: 2nd edDescripción: viii, 291 p. : il. ; 25 cmISBN: 0387962050Tema(s): Algebras, LinearOtra clasificación: 15-01 (65F05)CHAPTER I Vectors [1] §L Definition of Points in Space [1] §2. Located Vectors [9] $3. Scalar Product [12] §4. The Norm of a Vector [15] §5. Parametric Lines [30] §6. Planes [34] CHAPTER II Matrices and Linear Equations [42] §1. Matrices [43] §2. Multiplication of Matrices [47] §3. Homogeneous Linear Equations and Elimination [64] §4. Row Operations and Gauss Elimination [70] §5 Row Operations and Elementary Matrices [77] §6. Linear Combinations [85] CHAPTER III Vector Spaces [88] §1. Definitions. [88] §2. Linear Combinations [93] §3. Convex Sets. [99] §4- Linear Independence [104] §5. Dimension. [110] §6. The Rank of a Matrix [115] CHAPTER IV Linear Mappings [123] §1. Mappings [123] §2. Linear Mappings [127] §3. The Kernel and Image of a Linear Map [136] §4. The Rank and Linear Equations Again [144] §5. The Matrix Associated with a Linear Map [150] Appendix: Change of Bases [154] CHAPTER V Composition and Inverse Mappings [158] §1. Composition of Linear Maps [158] §2. Inverses [164] CHAPTER VI Scalar Products and Orthogonality [171] §1. Scalar Products [171] §2. Orthogonal Bases [180] $3. Bilinear Maps and Matrices [190] CHAPTER VII Determinants [195] §1. Determinants of Order 2 [195] §2 3 x 3 and n x n Determinants [200] §3. The Rank of a Matrix and Subdeterminants [210] §4. Cramer’s Rule [214] §5. Inverse of a Matrix [217] §6. Determinants as Area and Volume [221] CHAPTER VIII Eigenvectors and Eigenvalues [233] §1. Eigenvectors and Eigenvalues [233] §2. The Characteristic Polynomial [238] (3. Eigenvalues and Eigenvectors of Symmetric Matrices [250] $4. Diagonalization of a Symmetric Linear Map [255] Appendix. Complex Numbers [260] Answers to Exercises [265] Index [291]
| Item type | Home library | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | 15 L269i (Browse shelf) | Available | A-8490 |
Incluye índices.
CHAPTER I --
Vectors [1] --
§L Definition of Points in Space [1] --
§2. Located Vectors [9] --
$3. Scalar Product [12] --
§4. The Norm of a Vector [15] --
§5. Parametric Lines [30] --
§6. Planes [34] --
CHAPTER II --
Matrices and Linear Equations [42] --
§1. Matrices [43] --
§2. Multiplication of Matrices [47] --
§3. Homogeneous Linear Equations and Elimination [64] --
§4. Row Operations and Gauss Elimination [70] --
§5 Row Operations and Elementary Matrices [77] --
§6. Linear Combinations [85] --
CHAPTER III --
Vector Spaces [88] --
§1. Definitions. [88] --
§2. Linear Combinations [93] --
§3. Convex Sets. [99] --
§4- Linear Independence [104] --
§5. Dimension. [110] --
§6. The Rank of a Matrix [115] --
CHAPTER IV --
Linear Mappings [123] --
§1. Mappings [123] --
§2. Linear Mappings [127] --
§3. The Kernel and Image of a Linear Map [136] --
§4. The Rank and Linear Equations Again [144] --
§5. The Matrix Associated with a Linear Map [150] --
Appendix: Change of Bases [154] --
CHAPTER V --
Composition and Inverse Mappings [158] --
§1. Composition of Linear Maps [158] --
§2. Inverses [164] --
CHAPTER VI --
Scalar Products and Orthogonality [171] --
§1. Scalar Products [171] --
§2. Orthogonal Bases [180] --
$3. Bilinear Maps and Matrices [190] --
CHAPTER VII --
Determinants [195] --
§1. Determinants of Order 2 [195] --
§2 3 x 3 and n x n Determinants [200] --
§3. The Rank of a Matrix and Subdeterminants [210] --
§4. Cramer’s Rule [214] --
§5. Inverse of a Matrix [217] --
§6. Determinants as Area and Volume [221] --
CHAPTER VIII --
Eigenvectors and Eigenvalues [233] --
§1. Eigenvectors and Eigenvalues [233] --
§2. The Characteristic Polynomial [238] --
(3. Eigenvalues and Eigenvectors of Symmetric Matrices [250] --
$4. Diagonalization of a Symmetric Linear Map [255] --
Appendix. Complex Numbers [260] --
Answers to Exercises [265] --
Index [291] --
Zbl, 0577.15001
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