1. Use the result of Problem 17.15 to develop a function lq that performs the decomposition and test it with random matrices of sizes and Problem 17.15 Problem 17.14 presented the decomposition...

1.

Use the result of Problem 17.15 to develop a function lq that performs the

decomposition and test it with random matrices of sizes

and

Problem 17.15

Problem 17.14 presented the

decomposition of an

matrix


Implement the algorithm in a function ql and test it on at two matrices of different sizes.

If

is the

identity matrix,

gives the reversal matrix

_m
by rotating

⁰
counterclockwise.

Problem 17.14

Develop a MATLAB function

using Householder reflections that returns one of a set of possibilities according to the format of the calling sequence.

Use the MATLAB constructs

If you are not familiar with these, consult the MATLAB documentation. Test your function by constructing a
and a

matrix and using all the options on each.

2. In this problem, we will use computation to motivate a theoretical result.

Build a series of Givens rotations, and find the eigenvalues and corresponding eigenvectors for each. A pattern emerges.

Propose a formula for the eigenvalues and corresponding eigenvectors of a Givens rotation, and prove you are correct.