CHECKING THE VALIDITY OF D, G SCALING MATRICES

Consider Дб? scaling matrices, which satisfy at frequency wo:

( DM {jwo)D~l

  CHECKING THE VALIDITY OF D, G SCALING MATRICES

– )G F-1/4) < 1

 

(10.27)

 

p

  CHECKING THE VALIDITY OF D, G SCALING MATRICES CHECKING THE VALIDITY OF D, G SCALING MATRICES

and:

 

Let then:

 

CHECKING THE VALIDITY OF D, G SCALING MATRICES

Let tjm the real negative eigenvalue of % of maximal magnitude. Then:

1

uj = u)q H–

Vm

 

CHECKING THE VALIDITY OF D, G SCALING MATRICES

(10.34)

Let then r}p the real positive eigenvalue of mi of maximal magnitude. Then:

Подпись: (10.35)_ 1

u> = loq H

Op

Proof:

CHECKING THE VALIDITY OF D, G SCALING MATRICES

• Note as a preliminary that (see equation (10.31)):

and:

Fi(H(uo), 6ulm) = Hu + 6uHl2{Im ~ 6ljH22)-1H21 (10.36)

As a consequence:

F~1/4 1 _ f_1/4 = Ріфл6шІт) [10]

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