Linear algebra / G. Hadley.
Series Addison-Wesley series in mathematicsEditor: Reading, Mass. : Addison-Wesley, c1961Descripción: 290 p. : il. ; 24 cmOtra clasificación: 15-01Chapter 1. Introduction [1] 1-1 Linear models [1] 1-2 Linear algebra [2] 1-3 Leontief’s interindustry model of an economy [3] 1-4 Linear programming [6] 1-5 Graphical solution of a linear programming problem in two variables [8] 1-6 Regression analysis [10] 1-7 Linear circuit theory [12] 1-8 Other linear models [14] 1- 9 The road ahead [14] Chapter 2. Vectors [17] 2- 1 Physical motivation for the vector concept [17] 2-2 Operations with vectors [19] 2-3 The scalar product [22] 2-4 Generalization to higher dimensions [25] 2-5 Generalized vector operations [28] 2-6 Euclidean space and the scalar product [30] 2-7 Linear dependence [34] 2-8 The concept of a basis [39] 2-9 Changing a single vector in a basis [41] 2-10 Number of vectors in a basis for En [43] 2-11 Orthogonal bases [45] 2-12 Generalized coordinate systems [48] 2- 13 Vector spaces and subspaces [50] Chapter 3. Matrices and Determinants [60] 3- 1 Matrices [60] 3-2 Matrix operations [61] 3-3 Matrix multiplication—introduction [64] 3-4 Matrix multiplication—further development [68] 3-5 Vectors and matrices [71] 3-6 Identity, scalar, diagonal, and null matrices [73] 3-7 The transpose [70] 3-8 Symmetric and skew-symmetric matrices [78] 3-9 Partitioning of matrices [79] 3-10 Basic notion of a determinant [85] 3-11 General definition of a determinant [85] 3-12 Some properties of determinants [88] 3-13 Expansion by cofactors [90] 3-14 Additional properties of determinants [93] 3-15 Laplace expansion [95] 3-16 Multiplication of determinants [99] 3-17 Determinant of the product of rectangular matrices [100] 3-18 The matrix inverse [103] 3-19 Properties of the inverse [105] 3-20 Computation of the inverse by partitioning [107] 3-21 Product form of the inverse [111] 3-22 Matrix series and the Leontief inverse [116] Chapter 4. Linear Transformations, Rank, and Elementary Transformations [132] 4-1 Definition of linear transformations [132] 4-2 Properties of linear transformations [135] 4-3 Rank [138] 4-4 Rank and determinants [140] 4-5 Elementary transformations [144] 4- 6 Echelon matrices and rank [148] Chapter 5. Simultaneous Linear Equations [182] 5- 1 Introduction [162] 5-2 Gaussian elimination [162] 5-3 Cramer’s rule [166] 5-4 Rules of rank [167] 5-5 Further properties [170] 5-6 Homogeneous linear equations [173] 5-7 Geometric interpretation [177] 5- 8 Basic solutions [178] Chapter 6. Convex Sets and n-Dimensional Geometry [188] 6- 1 Sets [188] 6-2 Point sets [189] 6-3 Lines and hyperplanes [194] 6-4 Convex sets [202] 6-5 The convex hull [207] 6-6 Theorems on separating hyperplanes [210] 6-7 A basic result in linear programming [215] 6-8 Convex hull of extreme points [217] 6-9 Introduction to convex cones [219] 6-10 Convex polyhedral cones [224] 6-11 Linear transformations of regions [227] Chapter 7. Characteristic Value Problems and Quadratic Forms [236] 7-1 Characteristic value problems [236] 7-2 Similarity [238] 7-3 Characteristic value problems for symmetric matrices [239] 7-4 Additional properties of the eigenvectors of a symmetric matrix [242] 7-5 Diagonalization of symmetric matrices [247] 7-6 Characteristic value problems for nonsymmetric matrices [249] 7-7 Quadratic forms [251] 7-8 Change of variables [253] 7-9 Definite quadratic forms [254] 7-10 Diagonalization of quadratic forms [255] 7-11 Diagonalization by completion of the square [257] 7-12 Another set of necessary and sufficient conditions for positive and negative definite forms [259] 7-13 Simultaneous diagonalization of two quadratic forms [263] 7-14 Geometric interpretation; coordinates and bases [264] 7-15 Equivalence and similarity [267] 7-16 Rotation of coordinates; orthogonal transformations [269]
| Item type | Home library | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Libros
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Instituto de Matemática, CONICET-UNS | 15 H131 (Browse shelf) | Available | A-8196 |
Bibliografía al final de cada capítulo.
Chapter 1. Introduction [1] --
1-1 Linear models [1] --
1-2 Linear algebra [2] --
1-3 Leontief’s interindustry model of an economy [3] --
1-4 Linear programming [6] --
1-5 Graphical solution of a linear programming problem in two variables [8] --
1-6 Regression analysis [10] --
1-7 Linear circuit theory [12] --
1-8 Other linear models [14] --
1- 9 The road ahead [14] --
Chapter 2. Vectors [17] --
2- 1 Physical motivation for the vector concept [17] --
2-2 Operations with vectors [19] --
2-3 The scalar product [22] --
2-4 Generalization to higher dimensions [25] --
2-5 Generalized vector operations [28] --
2-6 Euclidean space and the scalar product [30] --
2-7 Linear dependence [34] --
2-8 The concept of a basis [39] --
2-9 Changing a single vector in a basis [41] --
2-10 Number of vectors in a basis for En [43] --
2-11 Orthogonal bases [45] --
2-12 Generalized coordinate systems [48] --
2- 13 Vector spaces and subspaces [50] --
Chapter 3. Matrices and Determinants [60] --
3- 1 Matrices [60] --
3-2 Matrix operations [61] --
3-3 Matrix multiplication—introduction [64] --
3-4 Matrix multiplication—further development [68] --
3-5 Vectors and matrices [71] --
3-6 Identity, scalar, diagonal, and null matrices [73] --
3-7 The transpose [70] --
3-8 Symmetric and skew-symmetric matrices [78] --
3-9 Partitioning of matrices [79] --
3-10 Basic notion of a determinant [85] --
3-11 General definition of a determinant [85] --
3-12 Some properties of determinants [88] --
3-13 Expansion by cofactors [90] --
3-14 Additional properties of determinants [93] --
3-15 Laplace expansion [95] --
3-16 Multiplication of determinants [99] --
3-17 Determinant of the product of rectangular matrices [100] --
3-18 The matrix inverse [103] --
3-19 Properties of the inverse [105] --
3-20 Computation of the inverse by partitioning [107] --
3-21 Product form of the inverse [111] --
3-22 Matrix series and the Leontief inverse [116] --
Chapter 4. Linear Transformations, Rank, and Elementary Transformations [132] --
4-1 Definition of linear transformations [132] --
4-2 Properties of linear transformations [135] --
4-3 Rank [138] --
4-4 Rank and determinants [140] --
4-5 Elementary transformations [144] --
4- 6 Echelon matrices and rank [148] --
Chapter 5. Simultaneous Linear Equations [182] --
5- 1 Introduction [162] --
5-2 Gaussian elimination [162] --
5-3 Cramer’s rule [166] --
5-4 Rules of rank [167] --
5-5 Further properties [170] --
5-6 Homogeneous linear equations [173] --
5-7 Geometric interpretation [177] --
5- 8 Basic solutions [178] --
Chapter 6. Convex Sets and n-Dimensional Geometry [188] --
6- 1 Sets [188] --
6-2 Point sets [189] --
6-3 Lines and hyperplanes [194] --
6-4 Convex sets [202] --
6-5 The convex hull [207] --
6-6 Theorems on separating hyperplanes [210] --
6-7 A basic result in linear programming [215] --
6-8 Convex hull of extreme points [217] --
6-9 Introduction to convex cones [219] --
6-10 Convex polyhedral cones [224] --
6-11 Linear transformations of regions [227] --
Chapter 7. Characteristic Value Problems and Quadratic Forms [236] --
7-1 Characteristic value problems [236] --
7-2 Similarity [238] --
7-3 Characteristic value problems for symmetric matrices [239] --
7-4 Additional properties of the eigenvectors of a symmetric matrix [242] --
7-5 Diagonalization of symmetric matrices [247] --
7-6 Characteristic value problems for nonsymmetric matrices [249] --
7-7 Quadratic forms [251] --
7-8 Change of variables [253] --
7-9 Definite quadratic forms [254] --
7-10 Diagonalization of quadratic forms [255] --
7-11 Diagonalization by completion of the square [257] --
7-12 Another set of necessary and sufficient conditions for positive and negative definite forms [259] --
7-13 Simultaneous diagonalization of two quadratic forms [263] --
7-14 Geometric interpretation; coordinates and bases [264] --
7-15 Equivalence and similarity [267] --
7-16 Rotation of coordinates; orthogonal transformations [269] --
MR, 22 #12107
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