Читать книгу Linear Algebra - Michael L. O'Leary - Страница 3

1 Chapter 1Figure 1.1 A function f ⊆ A × B .Figure 1.2 The composition of f and g.Figure 1.3 g is not a one‐to‐one function.Figure 1.4 h is a one‐to‐one function.Figure 1.5 f is an onto function.Figure 1.6 g is a bijection.Figure 1.7 The image of C under f.Figure 1.8 The inverse image of D under f.

2 Chapter 2Figure 2.1 Two interpretations of vector as an arrow.Figure 2.2 Addition of arrows.Figure 2.3 Scaling ofarrows.Figure 2.4 Finding the distance between vectors.Figure 2.5 A triangle in ℝ³ .Figure 2.6 The distance between u and v is ‖u − v‖...Figure 2.7 The line L containing u with direction vector m.Figure 2.8 The plane P containing u with direction vectors m and n.Figure 2.9 Lines L and L′ with normal n.Figure 2.10 u = r v + w with w orthogonal to v.Figure 2.11 The distance from the vector u to the plane P.Figure 2.12 The distance from the vector u to the plane P, side view.Figure 2.13 Computing the cross product.Figure 2.14 The parallelogram described by u and v.Figure 2.15 The parallelepiped described by u, v, and w.

3 Chapter 3Figure 3.1 Linear transformations preserve addition.Figure 3.2 Linear transformations preserve scalar multiplication.Figure 3.3 A reflection through the line ℓ.Figure 3.4 A reflection in ℝ² through the line L.Figure 3.5 A reflection in ℝ³ through the xy‐plane.Figure 3.6 A rotation of θ centered at O.Figure 3.7 A rotation in ℝ² through θ.Figure 3.8 A rotation in ℝ³ about the z‐axis through θ.Figure 3.9 A rotation in ℝ³ about the z‐axis through θ viewed fro...Figure 3.10 A rotation in ℝ³ of e ₃ and e ₁ about the y‐axis through θ...Figure 3.11 A reflection is an isometry.Figure 3.12 A rotation is an isometry.Figure 3.13 A translation is anisometry.Figure 3.14 A shear along L.Figure 3.15 A horizontal shear with shear factor k.

4 Chapter 4Figure 4.1 The parallelogram described by u and v.Figure 4.2 The parallelogram described by T u and T v.Figure 4.3 The areas of a parallelogram and its image under a linear operato...

5 Chapter 5Figure 5.1 Illustrating the Rank‐Nullity Theorem.Figure 5.2 Writing w as a linear combination of two bases.Figure 5.3 Change of basis Figure 5.4 Diagram for the change of basis transformation .Figure 5.5 Change of basis with linear transformation T.Figure 5.6 Diagram for the standard transformation .

6 Chapter 6Figure 6.1 The projection of u ₂ onto v ₁ .Figure 6.2 Finding a vector orthogonal to S(v ₁, v ₂). Figure 6.3 The projection of u ₃ onto v ₁ .

7 Chapter 7Figure 7.1 The ellipse 7x ² + 4xy + 4y ² = 16 wi...