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5) Let A be an n × n matrix. Show that any collection of eigenvectors of A corresponding to different eigenvalues is linearly independent. (Hint: Need show general case, can be proved directly or by induction)

5) Let A be an n × n matrix. Show that any collection of eigenvectors of A corresponding to different eigenvalues is linearly independent. (Hint: Need show general case, can be proved directly or by induction)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need prove linear independence of eigrnvectors.

I posted this before and just showed me with 2 vectors.

I need general case which apparantly can be proved directly.

 

Thanks

5) Let A be an n × n matrix. Show that any collection of eigenvectors of A corresponding to different eigenvalues is linearly independent. (Hint: Need show general case, can be proved directly or by induction)
Transcribed Image Text:5) Let A be an n × n matrix. Show that any collection of eigenvectors of A corresponding to different eigenvalues is linearly independent. (Hint: Need show general case, can be proved directly or by induction)
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