ECEN601_hw10_pfister

# ECEN601_hw10_pfister - A then 1/Î is an eigenvalue of A-1...

This preview shows page 1. Sign up to view the full content.

ECEN 601: Assignment 10 Problems: 1. Show that the determinant of an n × n matrix is the product of the eigenvalues; that is, det( A ) = n productdisplay i =1 λ i . 2. Show that the trace of a matrix is the sum of the eigenvalues, tr( A ) = n summationdisplay i =1 λ i . 3. Show that if λ * is an eigenvalue of A , then λ * + r is an eigenvalue of A + rI , and that A and A + rI have the same eigenvectors. 4. Suppose that A - 1 exists; prove the following statements. If
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: A then 1 /Î» is an eigenvalue of A-1 . The eigenvectors of A corresponding to nonzero eigenvalues are eigenvectors of A-1 . 5. Show that the eigenvalues of a projection matrix P are either 1 or 0. 6. Determine the Jordan forms of A 1 = 2 1 2 2 3 2 and A 2 = 2 2 2 3 2 . 1...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business â€˜17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. Itâ€™s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania â€˜17, Course Hero Intern

• The ability to access any universityâ€™s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLAâ€™s materials to help me move forward and get everything together on time.

Jill Tulane University â€˜16, Course Hero Intern