Contents
Preface fo r Instructor s i x
Acknowledgements xii i
Introduction 1
Chapter 1. Linea r Algebr a Revie w 5
§1.1. Vecto r Space s 5
§1.2. Base s fo r Vecto r Space s 8
§1.3. Linea r Operator s an d Matrice s 17
§1.4. Th e Ran k o f a Linea r Operato r an d a Matri x 2 3
§1.5. Determinan t an d Trac e 2 5
§1.6. Inne r Product s an d Orthonorma l Base s 2 7
§1.7. Orthogona l Direc t Su m 3 4
§1.8. Exercise s fro m th e Tex t 3 6
§1.9. Additiona l Exercise s 3 7
Chapter 2 . Finite-Dimensiona l Operato r Theor y 4 1
§2.1. Linea r Functional s an d th e Dua l Spac e 4 1
§2.2. Ries z Representatio n Theore m an d Adjoin t Operator s 4 3
§2.3. Self-adjoin t an d Unitar y Operator s 4 6
§2.4. Orthogona l Complement s an d Projection s 5 2
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