bidiagonal matrix is a matrix with nonzero entries along the main diagonal and either the diagonal above or the diagonal below. The matrix is an upper bidiagonal matrix and is a lower bidiagonal...

bidiagonal matrix is a matrix with nonzero entries along the main diagonal and either the diagonal above or the diagonal below. The matrix

is an upper bidiagonal matrix and

is a lower bidiagonal matrix.

tridiagonal matrix has only nonzero entries along the main diagonal and the diagonals above and below.

is a tridiagonal matrix

e will show in Chapter 13 that a nonsingular tridiagonal matrix can be factored into the product of a lower bidiagonal matrix and an upper bidiagonal matrix. The lower bidiagonal matrix has ones on its diagonal.

Using pencil and paper, verify that

Using the MATLAB command diag, build the tridiagonal matrix

as follows

The book software distribution supplies the function trifact that factors a tridiagonal matrix. Enter the following MATLAB statements and then verify that