My book writes the following statement:
For a square matrix $A$ of order $n$ to be diagonalizable, the sum of the dimensions of the eigenspaces must be equal to $n$. One way this can happen is when $A$ has $n$ distinct eigenvalues.
I'm a little confused on the last sentence. Are they trying to say that if $A$ has $n$ eigenvalues, then it must be the case that each eigenspace is $1$-dimensional? Couldn't it be possible for one or more of the eigenspaces to be $2$-dimensional or three-dimensional, etc?