The decomposition of an matrix is a decomposition of a matrix into a product where is an orthogonal matrix and is an upper-triangular matrix. We will extensively discuss this decomposition in...

The

decomposition of an

matrix is a decomposition of a matrix

into a product

where

is an orthogonal matrix and

is an upper-triangular matrix. We will extensively discuss this decomposition in Chapters 14 and 17. There are two types of

decomposition, the full and the reduced:

For

the reduced decomposition saves space. To obtain a reduced

decomposition, use the MATLAB function qr as follows:

For reasons we will explain in Chapter 16, if

and rank

one method of solving a least-squares problem is to follow these steps:

Implement solveq as a MATLAB function. Use backsolve from Chapter 9 to solve the upper-triangular system