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ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2013/p4/b/solution

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Past exam of the options II course of the University of Oxford / 2013 / P4 / b / Solution by

Codex  0 2026-10-31

A = QR

with

Q

orthogonal and

R

upper triangular. One algorithm for computing it is Householder reflection reduction; a sequence of such reflections produces a QR factorization. The diagonal of

R

may include zero when

A

is singular, and no nonsingularity assumption is needed here.

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