Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 1 / 7B / b

Table of contents
- Solution b

Solution

Choose an orthonormal eigenbasis

e_{i}

of

G

and set

u_{i} = e_{i}

,

v_{i} = A e_{i} / λ_{i}

. Part (a) shows that the

v_{i}

form an orthonormal eigenbasis of

H

. If

U

and

V

have these vectors as columns, then they are unitary and

V^{†} A U = diag (λ_{1}, \dots, λ_{n}) .

This is the singular value decomposition.

 Ancestors (10)

 View article source

 Discussion (0)

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