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H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/...

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H.Melikian/1200 Linear Algebra II Dr .Hayk Melikyan/ Departmen of Mathematics and CS/ [email protected] Linear Transformations and Matrices (Sec 2.7) Composition and Invertibility of Linear Transformations (Sec 2.8
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Page 1: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 1

Linear Algebra II

Dr .Hayk Melikyan/ Departmen of Mathematics and CS/ [email protected]

Linear Transformations and Matrices (Sec 2.7)

Composition and Invertibility of Linear Transformations (Sec 2.8

Page 2: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 2

Functions and Mappings

Page 3: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 3

Transformations Induced by Matrices

Page 4: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 4

Properties of Matrix Transformation

Page 5: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 5

Linear Transformations

Page 6: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 6

Properties of Linear Transformations

Page 7: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 7

Composition and Invertibility of Linear Transformations (Sec 2.8)

Page 8: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 8

Properties of onto Maps

Page 9: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 9

One-to-one maps and Null Space of Transformation

Page 10: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 10

Example.

Determine whether the given linear transformation is one-to-one, onto or both

Page 11: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 11

Composition of Maps

Page 12: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 12

Composition of Matrix transformations

Page 13: H.Melikian/12001 Linear Algebra II Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu Linear Transformations and Matrices (Sec 2.7) Composition.

H.Melikian/1200 13

Invertibility of Linear Transformation


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