1 cn 2 now sketch z1 z1 25 z

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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 non-negative on t...
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