1. Find the eigenvalues of a Householder reflection. Run some numerical experiments to look for a pattern. If u is a Householder reflection, u Starting with build a basis 12n and take note of part...

1.

Find the eigenvalues of a Householder reflection.

Run some numerical experiments to look for a pattern. If

_u
is a Householder reflection,

_u

Starting with

build a basis

<sub>1

2

n</sub>

and take note of part 4 in Theorem 17.3.

2.

Given


^T

build the Givens matrix

such that the second component of
is zero. Build the Givens matrix

such that

has the form

^T

Use a sequence like the following to explicitly build a Givens matrix.