Question: Show x x ( k ) < = T k / ( 1 T ) x ( 1 ) x ( 0 ) if ||T||

Show

xx(k)<= Tk/(1T)x(1)x(0)

if ||T||<1 for any matrix norm, where the sequence {x^(k)}inf k=0 is defined by

x^(k)=Tx^(k-1)+c

and c is a given vector

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