Eigenvectors and Row/Column Vectors: What's the Connection?

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SUMMARY

The discussion focuses on the relationship between eigenvectors of a matrix and its row or column vectors. Participants clarify that there is no general relation between these two concepts. The Gershgorin Circle Theorem is mentioned as a relevant resource for understanding eigenvalues and their implications. The conversation emphasizes the distinct nature of eigenvectors compared to the matrix's constituent vectors.

PREREQUISITES
  • Understanding of linear algebra concepts, particularly eigenvectors and eigenvalues.
  • Familiarity with matrix theory, including row and column vectors.
  • Knowledge of the Gershgorin Circle Theorem and its applications.
  • Basic proficiency in mathematical notation and terminology.
NEXT STEPS
  • Study the Gershgorin Circle Theorem in detail to understand its implications for eigenvalues.
  • Explore the properties of eigenvectors and their significance in linear transformations.
  • Investigate the relationship between eigenvalues and matrix diagonalization techniques.
  • Learn about applications of eigenvectors in fields such as machine learning and data analysis.
USEFUL FOR

Students and professionals in mathematics, particularly those studying linear algebra, as well as researchers and practitioners in fields utilizing matrix theory and eigenvalue analysis.

Mappe
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Is there a general between the eigenvectors of a matrix and the row (or column) vectors making up the matrix?
 
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General relation I meant off cause ;\
 
Mappe said:
Is there a general between the eigenvectors of a matrix and the row (or column) vectors making up the matrix?
Not that I'm aware of.
Mappe said:
General relation I meant off cause ;\
Do you mean, "of course"?
 

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