Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Complex eigenvalue proof
Reply to thread
Message
[QUOTE="Dusty912, post: 5445304, member: 577474"] [h2]Homework Statement [/h2] Suppose the matrix [B]A [/B]with real entries has the complex eigenvalue λ=α+iβ, β does not equal 0. Let [B]Y[SUB]0[/SUB] [/B]be an eigenvector for λ and write [B]Y[SUB]0[/SUB][/B]=[B]Y[SUB]1[/SUB] [/B]+i[B]Y[SUB]2[/SUB] [/B], where [B]Y[SUB]1[/SUB] [/B]=(x[SUB]1[/SUB], y[SUB]1[/SUB]) and [B]Y[SUB]2[/SUB] [/B]=(x[SUB]2[/SUB], y[SUB]2[/SUB]) have real entries. Show that [B]Y[SUB]1[/SUB] [/B]and [B]Y[SUB]2[/SUB] [/B]are linearly independent. [Hint: Suppose they are not linearly independent. Then (x[SUB]2[/SUB], y[SUB]2[/SUB])=k(x[SUB]1[/SUB], y[SUB]1[/SUB) for some constant k. Then [B]Y[SUB]0[/SUB][/B]=(1+ik)[B]Y[SUB]1[/SUB][/B]. Then use the fact that [B]Y[SUB]0[/SUB] [/B]is an eigenvector of [B]A [/B]and that [B]AY[SUB]1[/SUB] [/B] contains no imaginary part. [h2]Homework Equations[/h2] AY=λY [h2]The Attempt at a Solution[/h2] Honestly, not too sure where to start for this one. I know I should begin by considering the scenario where [B]Y[SUB]1[/SUB] [/B]and [B]Y[SUB]2[/SUB] [/B] are not linearly independent, but I do not know where I should begin with this information. Thanks for your help :)[/SUB] [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Complex eigenvalue proof
Back
Top