mathLinAlgebra5-07-draft

mathLinAlgebra5-07-draft - ARE211 Fall 2007 LECTURE#15 THU...

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

View Full Document Right Arrow Icon
Preliminary draft only: please check for final version ARE211, Fall 2007 LECTURE #15: THU, OCT 18, 2007 PRINT DATE: AUGUST 21, 2007 (LINALGEBRA5) Contents 3. Linear Algebra (cont) 1 3.23. Eigenvalues, eigenvectors and difference Equations 1 3. Linear Algebra (cont) 3.23. Eigenvalues, eigenvectors and difference Equations Tremendously important application of eigenvalues and eigenvectors relates to difference equations. Consider a system of linear homogeneous first-order difference equations of the form x t = A x t - 1 . Think of this as an infinite system of equations, one for each time period. Each initial vector generates a sequence of vectors { x 0 , x 1 . . . } s.t. t > 0 , x t = A x t - 1 : any such sequence is called a solution to the system what are the properties of these solutions: do they converge to some specific vector? A steady state/equilibrium/stationary solution to an equation system is a vector x satisfying x = A x . Familiar result is that given a system of difference equations of the form x t = A x t - 1 such
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern