Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Digital systems, linear algebra, introduction to formal proof / 4 / f / Solution

Collect the orthonormal vectors as columns and compute

R = Q^{T} A

. This gives the thin QR decomposition

Q = \frac{1}{2} 1111 1 - 1 - 1 1 1 - 1 1 - 1, R = 200420222 .

The inner products in part (e) prove

Q^{T} Q = I_{3}

; the column identities

a_{1} = 2 q_{1}

,

a_{2} = 4 q_{1} + 2 q_{2}

,

a_{3} = 2 q_{1} + 2 q_{2} + 2 q_{3}

prove

A = QR

.

 Ancestors (12)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version