hey wht if two out of three eigen values corresponding to a given matrix A are same. Can we directly conclude tht the eigen vectors aint diagonalisable??

Question

hey wht if two out of three eigen values corresponding to a given matrix A  are same. Can we directly conclude tht the eigen vectors aint  diagonalisable??

anonymous · Answer

Diagonalizability can fail only if there are repeated eigenvalues. However, matrices
with repeated eigenvalues may still be diagonalizable ( ex: identity matrix, situations when we have a p dimensional eigenspace corresponding to an eigenvalue with multiplicity p)

rishavraj · Answer

so its obvious tht if two eigen values r same then the two eigen vectors  corresponding to those values will be same :)) 
thanks @akitav

rishavraj · Answer

@ganeshie8