{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

eigen vec&amp; val

# eigen vec&amp; val - Harvey Mudd College Math Tutorial...

This preview shows pages 1–2. Sign up to view the full content.

Harvey Mudd College Math Tutorial: Eigenvalues and Eigenvectors We review here the basics of computing eigenvalues and eigenvectors. Eigenvalues and eigenvectors play a prominent role in the study of ordinary differential equations and in many applications in the physical sciences. Expect to see them come up in a variety of contexts! Definitions Let A be an n × n matrix. The number λ is an eigenvalue of A if there exists a non-zero vector v such that A v = λ v . In this case, vector v is called an eigen- vector of A corresponding to λ . Computing Eigenvalues and Eigenvectors We can rewrite the condition A v = λ v as ( A - λI ) v = 0 . where I is the n × n identity matrix. Now, in order for a non-zero vector v to satisfy this equation, A - λI must not be invertible. That is, the determinant of A - λI must equal 0. We call p ( λ ) = det( A - λI ) the characteristic polynomial of A . The eigenvalues of A are sim- ply the roots of the characteristic polynomial of A . Otherwise, if A - λI has an inverse, ( A - λI ) - 1 ( A - λI ) v = ( A - λI ) - 1 0 v = 0 . But we are looking for a non-zero vector v .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the 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 ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’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 ‘17, Course Hero Intern

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

Jill Tulane University ‘16, Course Hero Intern