combinepdf-min-0193.pdf

combinepdf-min-0193.pdf - Notes on linear algebra(Monday...

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Unformatted text preview: Notes on linear algebra (Monday 17th October, 2016, 23:10) page 40 Notice that AP, AWL. . . , A? are a + 1 — p matrices. In other words, Apr Ap+1v . . , Ag are k matrices (since 11 = q -|— 1 m p). Denote these It matrices by Bl, 32,. . . , Bk. Thus, Bk 2 Ap—l—l—k for every k 6 {1,2, . . . ,h} i (27) Leti E {1,2,...,a} andj E {1,2,...,m}. We have it h I; Bk = 1:21 Ap—1+k = Ap 4" Ap+l + ' ' ' + Ap—l-l—h : =Ap—1+ic : 093187)) =AP+AP+1+---+Aq (sincepm1+h=a) = 2 AR (28) ...
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