The Wilkinson bidiagonal matrix has the general form and is often used for testing purposes.  Create an anonymous function using diag that builds an n × n Wilkinson bidiagonal matrix.  Graph the...

The Wilkinson bidiagonal matrix has the general form

and is often used for testing purposes.

 Create an anonymous function using diag that builds an n × n Wilkinson bidiagonal matrix.

 Graph the condition number of the Wilkinson bidiagonal matrices of orders 1 through 15. What are your conclusions?

 Eigenvalues are tricky to compute accurately. The
Wilkinson-bidiagonal matrix,
 has eigenvalues
 This matrix illustrates that even though the eigenvalues of a matrix are not equal or even close to each other, an eigenvalue problem can be ill-conditioned. Compute the eigenvalues of perturb
 by
 and compute the eigenvalues. Comment on the results.