VI
Contents
§2.5. Th e Moore-Penros e Invers e 5 9
§2.6. Eigenvalue s fo r Operator s 6 0
§2.7. Squar e Root s o f Positiv e Operator s 6 7
§2.8. Th e Pola r Decompositio n 6 9
§2.9. Trace s o f Operator s 7 2
§2.10. Th e Operato r Nor m 7 4
§2.11. Th e Spectra l Theore m 7 7
§2.12. Exercise s fro m th e Tex t 8
§2.13. Additiona l Exercise s 8 2
Chapter 3 . Introductio n t o Finit e Frame s 8 7
§3.1. M
n-Frames
8 8
§3.2. Parseva l Frame s 9 2
§3.3. Genera l Frame s an d th e Canonica l Reconstructio n
Formula 9 8
§3.4. Frame s an d Matrice s 104
§3.5. Similarit y an d Unitar y Equivalenc e o f Frame s 109
§3.6. Fram e Potentia l 13
§3.7. Numerica l Algorithm s 18
§3.8. Exercise s fro m th e Tex t 12
§3.9. Additiona l Exercise s 12
Chapter 4 . Frame s i n R
2
123
§4.1. Diagra m Vector s 123
§4.2. Equivalenc e o f Frame s 125
§4.3. Uni t Tigh t Frame s wit h Fou r Vector s 129
§4.4. Uni t Tigh t Frame s wit h k Vector s 13
§4.5. Fram e Surgery : Removal s an d Replacement s 134
§4.6. Fundamenta l Inequalit y i n R 2 137
§4.7. Exercise s fro m th e Tex t 138
§4.8. Additiona l Exercise s 139
Chapter 5 . Th e Dilatio n Propert y o f Frame s 14
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