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| Editor's Preface | |
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| Translators' Preface | |
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| Authors' Preface | |
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| Affine Space; Linear Equations | |
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| n-dimensional Affine Space | |
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| Vectors | |
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| The Concept of Linear Dependence | |
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| Vector Spaces in R<sub>n</sub> | |
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| Linear Spaces | |
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| Linear Equations | |
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| Homogeneous Linear Equations | |
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| Non-homogeneous Linear Equations | |
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| Geometric Applications | |
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| Euclidean Space; Theory of Determinants | |
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| Euclidean Length | |
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| Calculating with the Summation Sign | |
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| Volumes and Determinants | |
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| Fundamental Properties of Determinants | |
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| Existence and Uniqueness of Determinants | |
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| Volumes | |
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| The Principal Theorems of Determinant Theory | |
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| The Complete Development of a Determinant | |
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| The Determinant as a Function of its Column Vectors | |
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| The Multiplication Theorem | |
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| The Development of a Determinant by Rows or Columns | |
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| Determinants and Linear Equations | |
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| Laplace's Expansion Theorem | |
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| Transformation of Coordinates | |
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| General Linear Coordinate Systems | |
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| Cartesian Coordinate Systems | |
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| Continuous Deformation of a Linear Coordinate System | |
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| Construction of Normal Orthogonal Systems and Applications | |
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| Rigid Motions | |
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| Rigid Motions in R<sub>2</sub> | |
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| Rigid Motions in R<sub>3</sub> | |
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| Affine Transformations | |
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| Field Theory; The Fundamental Theorem of Algebra | |
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| The Concept of a Field | |
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| Polynomials over a Field | |
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| The Field of Complex Numbers | |
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| The Fundamental Theorem of Algebra | |
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| Elements of Group Theory | |
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| The Concept of a Group | |
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| Subgroups; Examples | |
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| The Basis Theorem for Abelian Groups | |
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| Linear Transformations and Matrices | |
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| The Algebra of Linear Transformations | |
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| Calculation with Matrices | |
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| Linear Transformations Under a Change of Coordinate System | |
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| The Determinant of a Linear Transformations | |
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| Linear Dependence of Matrices | |
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| Calculation With Matrix Polynomials | |
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| The Transpose of a Matrix | |
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| The Minimal Polynomial; Invariant Subspaces | |
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| The Minimal Polynomial | |
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| Invariant Subspaces | |
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| The Nullspace of a Linear Transformation f(�) | |
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| Decomposition of L into Invariant Subspaces | |
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| Geometric Interpretation | |
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| The Diagonal Form and its Applications | |
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| Unitary Transformations | |
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| Orthogonal Transformations | |
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| Hermitian and Symmetric Matrices (Principal Axis Transformations) | |
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| The Elementary Divisors of a Polynomial Matrix | |
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| The Normal Form | |
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| Consequences | |
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| Linear Transformation with Prescribed Elementary Divisors | |
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| The Jordan Normal Form | |
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| Index | |