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**notes.tex
(./notes.tex
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\OT1/cmr/m/it/10.95 prod-uct space and let $\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/1
0.95 e[]\OT1/cmr/m/n/10.95 )$ \OT1/cmr/m/it/10.95 be an or-thonor-mal se-quence
 in $\OML/cmm/m/it/10.95 X$\OT1/cmr/m/it/10.95 , and sup-pose $\OML/cmm/m/it/10
.95 x \OMS/cmsy/m/n/10.95 2 [] []$
 []

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\OT1/cmr/m/it/10.95 Problem \OT1/cmr/m/n/10.95 20 (Gram-m-Schmidt)\OT1/cmr/m/it
/10.95 . \OT1/cmr/m/n/10.95 Or-thonor-mal-ize the first three terms of the se-q
uence $(1\OML/cmm/m/it/10.95 ; t; t[]; t[]; [] \OT1/cmr/m/n/10.95 )$
 []

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[]\OT1/cmr/m/n/10.95 We have $(\OML/cmm/m/it/10.95 ST\OT1/cmr/m/n/10.95 )[] = \
OML/cmm/m/it/10.95 T[]S[]$ \OT1/cmr/m/n/10.95 be-cause $((\OML/cmm/m/it/10.95 S
T\OT1/cmr/m/n/10.95 )[]\OML/cmm/m/it/10.95 g\OT1/cmr/m/n/10.95 )(\OML/cmm/m/it/
10.95 x\OT1/cmr/m/n/10.95 ) = \OML/cmm/m/it/10.95 g\OT1/cmr/m/n/10.95 ((\OML/cm
m/m/it/10.95 ST\OT1/cmr/m/n/10.95 )(\OML/cmm/m/it/10.95 x\OT1/cmr/m/n/10.95 )) 
= \OML/cmm/m/it/10.95 g\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 S\OT1/cmr/m/n/10
.95 (\OML/cmm/m/it/10.95 T\OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 x\OT1/cmr/m/n
/10.95 ))) = (\OML/cmm/m/it/10.95 s[]g\OT1/cmr/m/n/10.95 )(\OML/cmm/m/it/10.95 
Tx\OT1/cmr/m/n/10.95 ) =
 []

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Overfull \hbox (36.0886pt too wide) in paragraph at lines 48--51
[]\OT1/cmr/m/n/10.95 Suppose that $\OML/cmm/m/it/10.95 T[]$ \OT1/cmr/m/n/10.95 
ex-ists and let $\OMS/cmsy/m/n/10.95 f\OML/cmm/m/it/10.95 e[]; e[]; :::; e[]\OM
S/cmsy/m/n/10.95 g$ \OT1/cmr/m/n/10.95 a ba-sis for $\OML/cmm/m/it/10.95 X$\OT1
/cmr/m/n/10.95 . We show that $\OMS/cmsy/m/n/10.95 f\OML/cmm/m/it/10.95 Te[]; T
e[]; :::; Te[]\OMS/cmsy/m/n/10.95 g$
 []

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Output written on notes.dvi (97 pages, 300880 bytes).