When to use RREF in finding Eigenvectors

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SUMMARY

Using Row Reduced Echelon Form (RREF) can simplify the process of finding eigenvectors by allowing for easier representation of systems in parametric vector form. While RREF is not necessary for determining eigenvalues, it can be beneficial in certain contexts where clarity in the solution set is required. The discussion highlights that row echelon form may suffice in many cases, but RREF provides a more structured approach when needed.

PREREQUISITES
  • Understanding of eigenvalues and eigenvectors
  • Familiarity with matrix operations
  • Knowledge of Row Reduced Echelon Form (RREF)
  • Concept of row echelon form
NEXT STEPS
  • Study the differences between Row Echelon Form and Row Reduced Echelon Form
  • Learn how to compute eigenvalues and eigenvectors using matrix transformations
  • Explore applications of RREF in solving linear systems
  • Investigate the implications of using RREF on the eigenvalues of a matrix
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Students and professionals in mathematics, particularly those studying linear algebra, as well as educators looking for clarification on the use of RREF in eigenvector calculations.

selig5560
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Hi,

I have a quick question, when should one use RREF in finding eigvenvectors? I've read through some books and sometimes they use them and sometimes they do not. I'm sorry for such a potentially stupid question.

Thanks,

Zubin
 
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It could be that having one in the pivot position position makes it easier to write system in parametric vector form. Otherwise row echelon form would suffice.
 
Last edited:
Where did you find that "they sometimes use them"? The row reduced form of a matrix does NOT in general have the same eigenvalues as the original matrix so I do see how row reducing could help.
 

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