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1 Chapter 4 Linear Transformations Definition and Examples Matrix Representations of Linear Transformations Similarity

Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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Page 1: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

1

Chapter 4 Linear Transformations

Definition and Examples

Matrix Representations of Linear Transformations

Similarity

Page 2: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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1. Definition and Examples

Page 3: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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1. Definition and Examples

Page 4: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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1. Definition and Examples

Page 5: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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1. Definition and Examples

Page 6: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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1. Definition and Examples

Page 7: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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1. Definition and Examples

Page 8: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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1. Definition and Examples

Page 9: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

9

1. Definition and Examples

Page 10: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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1. Definition and Examples

Page 11: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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1. Definition and Examples

Page 12: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

12

1. Definition and Examples

Page 13: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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1. Definition and Examples

Page 14: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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Page 15: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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2. Matrix Representations of Linear

Transformations

Page 16: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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2. Matrix Representations of Linear

Transformations

Page 17: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

17

2. Matrix Representations of Linear

Transformations

Page 18: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

18

2. Matrix Representations of Linear

Transformations

Page 19: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

19

2. Matrix Representations of Linear

Transformations

Page 20: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

20

2. Matrix Representations of Linear

Transformations

Page 21: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

21

2. Matrix Representations of Linear

Transformations

Page 22: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

22

2. Matrix Representations of Linear

Transformations

Page 23: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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2. Matrix Representations of Linear

Transformations

Page 24: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

24

2. Matrix Representations of Linear

Transformations

Page 25: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

25

2. Matrix Representations of Linear

Transformations

Page 26: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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3. Similarity

Page 27: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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3. Similarity

Page 28: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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3. Similarity

Page 29: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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3. Similarity

Page 30: Definition and Examples Transformationscmliu/Courses/LA/chap04.pdf · Example 13 Let D : P3 P3 be the differentiation operator defined by D(p(x)) p' (x) The kernel of D consists of

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4. Concluding Remarks

Definition and Examples

Matrix Representations of Linear Transformations

Similarity