We have studied the and the s. There are many more, and the book will construct additional ones in later chapters. This problem develops two variants of the decomposition, the and the An matrix...

We have studied the

and the
s. There are many more, and the book will construct additional ones in later chapters. This problem develops two variants of the

decomposition, the

and the

An
matrix of the form

where

_i,m−i+1

and all other entries are zero is termed a reversal matrix and sometimes the reverse identity matrix.

where

is an

matrix with orthogonal columns, and

is an

lower triangular matrix.

This is a reduced

decomposition.

If

show to form an

decomposition,

where

is

and

is