- #1
db1uover
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Homework Statement
Let V be a n-dimensional real vector space and L: V --> V be a linear operator. Then,
A.) L can always be diagonalized
B.) L can be diagonalized only if L has n distinct eigenvalues
C.) L can be diagonalized if all the n eigenvalues of L are real
D.) Knowing the eigenvalues is always enough to decide if L can be diagonalized or not
E.) L can be diagonalized if all its n eigenvalues are distinct
Homework Equations
I have the answer, but I don't understand the slight differences between 'only if L has n distinct eigenv' and 'if all its n eigenv are distinct'. Can someone explain how the statements have different meanings?
The Attempt at a Solution
Starting with the assumption that the statements are different, I understood it as Ans B means must have only n eigenv while Ans E is slightly more flexible in its requirements. Is this correct? Is there more to the story?