| CHAPTER 1 Introduction to Matrix Algebra 1.1 Matrices 1.2 Equality of Matrices 1.3 Addition of Matrices 1.4 Commutative and Associative Laws of Addition 1.5 Subtraction of Matrices 1.6 Scalar Multiples of Matrices 1.7 The Multiplication of Matrices 1.8 The Properties of Matrix Multiplication 1.9 Exercises 1.10 Linear Equations in Matrix Notation 1.11 The Transpose of a Matrix 1.12 Symmetric, Skew-Symmetric, and Hermitian Matrices 1.13 Scalar Matrices 1.14 The Identity Matrix 1.15 The Inverse of a Matrix 1.16 The Product of a Row Matrix into a Column Matrix 1.17 Polynomial Functions of Matrices 1.18 Exercises 1.19 Partitioned Matrices 1.20 Exercises 2 Linear Equations 2.1 Linear Equations 2.2 Three Examples 2.3 Exercises 2.4 Equivalent Systems of Equations 2.5 The Echelon Form for Systems of Equations 2.6 Synthetic Elimination 2.7 Systems of Homogeneous Linear Equations 2.8 Exercises 2.9 Computation of the Inverse of a Matrix 2.10 Matrix Inversion by Partitioning 2.11 Exercises 2.12 Number Fields 2.13 Exercises 2.14 The General Concept of a Field 2.15 Exercises 3 Vector Geometry in 83 3.1 Geometric Representation of Vectors in 3.2 Operations on Vectors 3.3 Isomorphism 3.4 Length, Direction, and Sense 3.5 Orthogouality of Two Vectors 3.6 Exercises 3.7 The Vector Equation of a Line 3.8 The Vector Equation of a Plane 3.9 Exercises 3.10 Linear Combinations of Vectors in 3.11 Linear Dependence of Vectors; Bases 3.12 Exercises 4 Vector Geometry in n-Dimensional Space 4.1 The Real n-Space 4.2 Vectors in 4.3 Lines and Planes in 4.4 Linear Dependence and Independence in 4.5 Vector Spaces in 4.6 Exercises 4.7 Length and the Canchy-Schwarz Inequality 4.8 Angles and Orthogonality in 4.9 Half-Lines and Directed Distances 4.10 Unitary n-Space …… 5 Vector Spaces 6 The Rank of a Matrix 7 Determinants 8 Linear Transformations 9 The Characteristic Value Problem 10 Quadratic,Bilinear, and Hermitian Forms APPENDIX BIBLIOGRAPHY INDEX |
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