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Householder transformation

1.
Starting with the matrix on the bottom of page 388, use Maple to perform Householder transformations, generating a tridiagonal matrix that is similar to A.

2.
Use eigenvalues to find the eigenvalues of A and the tridiagonal matrix, and confirm that they are similar.

Hint: Make one of the elements of the matrix a floating-point number, then eigenvalues will run faster and return numerical answers. Also, subsequent calculations will be done in FP without your having to put evalf's all over the place.



Allen B. Downey
1998-11-02