How do u show that a matrix is diagonizable?

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Discussion Overview

The discussion revolves around methods to demonstrate that a matrix is diagonalizable. It includes various theoretical approaches and criteria relevant to linear algebra.

Discussion Character

  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant suggests finding a basis of eigenvectors as a primary method to show diagonalizability.
  • Another participant mentions several criteria, including demonstrating that the minimal polynomial has rank n, finding n distinct eigenvalues, and conditions related to the field being algebraically closed or the matrix being hermitian.
  • A later reply references a resource with standard criteria for diagonalizability.

Areas of Agreement / Disagreement

Participants present multiple methods and criteria for demonstrating diagonalizability, indicating that there is no single agreed-upon approach. The discussion remains unresolved regarding the best or most comprehensive method.

Contextual Notes

Some methods mentioned depend on specific conditions, such as the nature of the eigenvalues or the properties of the matrix (e.g., hermitian). The discussion does not resolve which criteria are universally applicable.

himurakenshin
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How do u show that a matrix is diagonizable ?
Thanks
 
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by finding a basis of eigenvectors, by demonstrating that its minimal polynomial has rank n (where the matrix is nxn), occasionally by finding n distinct eigenvalues, or sometimes by showing that the field is algebraically closed and the matrix is in the image of some group homomorphism, or perhaps in some cases by showing that it is hermitian...

just show that it has a basis of eigenvectors, ok?
 
ok thanks a lot
 
read my short book posted near here for several different standard criteria for diagonalizability.
 

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