Find out if nxn matrix is diagonalisable based on det(XI-A)

  • Thread starter Fairy111
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  • #1
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Homework Statement



If you need to check whether an nxn matrix, A, is diagonalisable or not, do you just find out what det(XI-A) is, and then if X has n distinct values it is diagonalisable, otherwise it's not.



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The Attempt at a Solution

 

Answers and Replies

  • #2
matt grime
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Consider the identity matrix...
 
  • #3
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The identity matrix has only one distinct solution, 1, but it is diagonalisable...

So how do you go about checking whether or not a matrix is diagonalisable or not?
 
  • #4


A nxn square matrix is diagonizable if it has n linearly independent eigenvectors. Having n distinct eigenvalues is sufficient but not necessary for diagonalizability.
 

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