hi,
what does it mean to say that a matrix A is diagonalizable iff R^n has a basis consisting of eigenvectors for A?
If is such a basis then,
If we denote
then
This means i.e. is similar to a diagonal matrix (definition of diagonalizable matrix).
Try to prove the reciprocal statement, if a is diagonalizable then ...
Regards.
Fernando Revilla
If is similar to a diagonal matrix , (that is there exists invertible such that ) try to prove that the columns of determine a basis of eigenvectors)
Hint: is equivalent to .
Regards.
Fernando Revilla