## Linear Operators: Spectral theory |

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Page 1017

calculate the trace of A relative to the

24 , 95 = c + Žasy , AC - 1 Yi = Ax ; = a ; ; X ; = 0 sa ; sY ; , j = 1 j = 1 and so , CAC -

yi = £aijYz . j = 1 From this it follows that the trace of CAC - 1 , calculated relative ...

calculate the trace of A relative to the

**basis**yz , . . . , Yn . Note that 40 + ų , – 45 –24 , 95 = c + Žasy , AC - 1 Yi = Ax ; = a ; ; X ; = 0 sa ; sY ; , j = 1 j = 1 and so , CAC -

yi = £aijYz . j = 1 From this it follows that the trace of CAC - 1 , calculated relative ...

Page 1029

Let S be an n - 1 dimensional subspace of En such that S 2 S . Then , since S is

necessarily invariant under T , there exists by the inductive hypothesis , an

orthonormal

Xn be ...

Let S be an n - 1 dimensional subspace of En such that S 2 S . Then , since S is

necessarily invariant under T , there exists by the inductive hypothesis , an

orthonormal

**basis**{ x1 , . . . , Xn - 1 } for S with ( ( T - ÀI ) xi , æ ; ) = 0 for j > i . LetXn be ...

Page 1344

It is readily seen , by a similar argument , that qi ( a ) depends continuously on 2 .

It then follows easily from Corollary X . 7 . 3 that E ; ( 2 ) = E ( M ( 2 ) ; 4 ; ( 2 ) )

depends continuously on 2 , i = 1 , . . . , k . Let v1 , . . . , v , be an orthonormal

...

It is readily seen , by a similar argument , that qi ( a ) depends continuously on 2 .

It then follows easily from Corollary X . 7 . 3 that E ; ( 2 ) = E ( M ( 2 ) ; 4 ; ( 2 ) )

depends continuously on 2 , i = 1 , . . . , k . Let v1 , . . . , v , be an orthonormal

**basis**...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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