Understanding Degenerate Eigenvalues and Vectors in Math Operations

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Homework Help Overview

The discussion revolves around the topic of degenerate eigenvalues and eigenvectors in the context of linear algebra, specifically focusing on matrices H and B. The original poster seeks clarification on why the matrices do not uniquely specify their eigenvectors despite having calculated them.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster has calculated eigenvalues and vectors for matrices H and B and questions the uniqueness of the eigenvectors due to degeneracy. Other participants express difficulty in finding three common eigenvectors and seek further understanding of the underlying reasons.

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Homework Statement



please see attached


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The Attempt at a Solution



Ok so I've done A and have worked out eigenvalues and vectors of H and B

For H I get 4 possible eigenvectors (1,0,0) (0,1,1) (0,0,1) and (0,1,0) . The q is why does neither matrix uniquely specify its eigenvectors? I guess the answer is because the eigenvalues are degenrate (repeated)..but is there a clearer explanation as to why?

Thanks
 

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Also - i can't seem to find three common eigen vectors.. I can only find (1,0,0) and (0.1.1)
 


anyoneeee?
 


why can't i find three common eigenvectors?
 

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