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Unformatted text preview: is, thus giving a unitary U . Then, for each inserted column, we adjust the corresponding row
˜
in R to zero, where ˜
R= 1
c1
1
c2
..
.
1
cn 2 Now, sketch: z1 · · · = z1 · · · 2.5 z j −1 zn 0
zj +1 · · ·
↑
j th column zj −1 zj zj +1 · · ·
ˆ zn 1
c1 1
c1 1
c2
.. .
1
cn 0 ...
1
cj − 1 0
1
cj +1
0 ···
... 0 1
cn Consequences of QR Factorization 2.5.2 Theorem (Cholesky). If B ∈ Mn satisﬁes B = A∗ A for A ∈ Mn then B = LL∗ with
L ∈ Mn a lower triangular and nonnegative on t...
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 Fall '12
 BernhardBodmann
 Math, Matrices

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