{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

The system has an unstable eigendirection along

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

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

Unformatted text preview: zero such that x x x . Then 0. Now let z x x x . Then clearly, z is a solution of x P x , with z . Furthermore, y 0 is also a solution, with y . By the uniqueness theorem, z y 0 Hence x x on the entire interval 9 . Let y 0 . Going in the other direction is trivial. be any solution of x z x y P x x . It follows that x is also a solution. Now let x y . Then the collection of vectors x x x y constitutes vectors, each with components. Based on the assertion in Prob. Section , these vectors are necessarily linearly dependent. That is, there are constants not all zero such that x x x y x y , 0. From Prob. , we have x x 0 for all Now , otherwise that would contradict the fact that the first vectors are linearly independent. Hence y x x x , and the assertion is true. . Consider z have x z x x x x , and suppose that we also x Based on the assumption, ________________________________________________________________________ page 364 —————————————————————————— CHAPTER 7. —— x x x 0. The collection of vectors x is linearly independe...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online