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Difference between revisions of "Linear Algebra (Book)"

Linear Algebra (Book) (view source)

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! Chapter/Section # !! Title !! Page #
! Chapter/Section # !! Title !! Page #
|-  
|-  
! colspan="3" | Chapter 1: Determinants
! colspan="3" | Chapter 1: DETERMINANTS
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| 1.1 || Number Fields || 1
| 1.1 || Number Fields || 1
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| || Problems || 28
| || Problems || 28
|-  
|-  
! colspan="3" | Chapter 2: Linear Equations
! colspan="3" | Chapter 2: LINEAR SPACES
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|-
| 1 || Equations in two unknowns || 53
| 2.1 || Definitions || 31
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| 2 || Equations in three unknowns || 57
| 2.2 || Linear Dependence || 36
|-
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! colspan="3" | Chapter 3: Real Numbers
| 2.3 || Bases, Components, Dimension || 38
|-
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| 1 || Addition and multiplication || 61
| 2.4 || Subspaces || 42
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| 2 || Real numbers: positivity || 64
| 2.5 || Linear Manifolds || 49
|-
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| 3 || Powers and roots || 70
| 2.6 || Hyperplanes || 51
|-
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| 4 || Inequalities || 75
| 2.7 || Morphisms of Linear Spaces || 53
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! colspan="3" | Chapter 4: Quadratic Equations
| || Problems || 56
|-
|-
! colspan="3" | Interlude: On Logic and Mathematical Expressions
! colspan="3" | Chapter 3: SYSTEMS OF LINEAR EQUATIONS
|-
|-
| 1 || On reading books || 93
| 3.1 || More on the Rank of a Matrix || 58
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| 2 || Logic || 94
| 3.2 || Nontrivial Compatibility of a Homogeneous Linear System || 60
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| 3 || Sets and elements || 99
| 3.3 || The Compatibility Condition for a General Linear System || 61
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| 4 || Notation || 100
| 3.4 || The General Solution of a Linear System || 63
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! colspan="3" | PART II: INTUITIVE GEOMETRY
| 3.4 || Geometric Properties of the Solution Space || 65
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! colspan="3" | Chapter 5: Distance and Angles
| 3.4 || Methods for Calculating the Rank of a Matrix || 67
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| 1 || Distance || 107
| || Problems || 71
|-
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| 2 || Angles || 110
! colspan="3" | Chapter 4: LINEAR FUNCTIONS OF A VECTOR ARGUMENT
|-
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| 3 || The Pythagoras theorem || 120
| 4.1 || Linear Forms || 75
|-
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! colspan="3" | Chapter 6: Isometries
| 4.2 || Linear Operators || 77
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| 4.3 || Sums and Products of Linear Operators || 82
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| 4.4 || Corresponding Operations on Matrices || 84
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| 4.5 || Further Properties of Matrix Multiplication || 88
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| 4.6 || The Range and Null Space of a Linear Operator || 93
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| 4.7 || Linear Operators Mapping a Space \(K_n\) into Itself || 98
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| 4.8 || Invariant Subspaces || 106
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| 4.9 || Eigenvectors and Eigenvalues || 108
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| || Problems|| 113
|-
! colspan="3" | Chapter 5: COORDINATE TRANSFORMATIONS
|-
| 5.1 || Transformation to a New Basis || 118
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| 5.2 || Consecutive Transformations || 120
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| 5.3 || Transformation of the Components of a Vector  || 121
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| 5.4 || Transformation of the Coefficients of a Linear Form || 123
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| 5.5 || Transformation of the Matrix of a Linear Operator || 124
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| *5.6 || Tensors || 126
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| || Problems || 131
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! colspan="3" | Chapter 6: THE CANONICAL FORM OF THE MATRIX OF A LINEAR OPERATOR
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| 1 || Some standard mappings of the plane || 133
| 1 || Some standard mappings of the plane || 133
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