## Linear Operators: General theory |

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Page 251

It is clear that E is a

D is an orthogonal

M ...

It is clear that E is a

**projection**, i . e . , E2 = E , and that E is an orthogonal**projection**. It is the uniquely determined orthogonal**projection**with EH = M . For ifD is an orthogonal

**projection**with DH = M then ED = D and , since ( I - D ) H CHOM ...

Page 514

19 If E is a

dimensional range . 20 A

compact . 21 A linear mapping E such that E2 = E is a

bounded ) ...

19 If E is a

**projection**with n dimensional range , then E * is a**projection**with ndimensional range . 20 A

**projection**has finite dimensional range if and only if it iscompact . 21 A linear mapping E such that E2 = E is a

**projection**( i.e. , isbounded ) ...

Page 515

Nelson Dunford, Jacob T. Schwartz, William G. Bade. ( i ) If E is a perpendicular

{ n - 1 Pikex , k = 1 , ... , ” is any orthonormal basis of M E ( X ) . ( ii ) Let M and N ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade. ( i ) If E is a perpendicular

**projection**, show that its matrix representation is ( ajj ) = ( Ex - iPixPik ) , where gx{ n - 1 Pikex , k = 1 , ... , ” is any orthonormal basis of M E ( X ) . ( ii ) Let M and N ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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