As in the title, lets say i have a matrix wich have the characteristic poyinomial with degree $(n)$ and lets say the degree of his minimal polynomial is $(n-1)$. This fact influence the possibilities of diagonalization?
And if the polynomials have the same degree? This tell us something about we can or not diagonalize those matrices?
I will say... ...no. In both cases. I'm wrong?
In general, "no" is correct. The exception are $n=1$ and $n=2$: if the characteristic polynomial has degree $1$ or if the minimal polynomial has degree $1$, the matrix is certainly diagonalizable.
Over the complex numbers, a matrix is diagonalizable iff its minimal polynomial has all roots distinct.
The characteristic polynomial of an $n \times n$ matrix has degree $n$. Thus if there are $k$ distinct eigenvalues (roots of the characteristic polynomial), the matrix is diagonalizable iff the minimal polynomial has degree $k$. But $k$ could be anywhere from $1$ to $n$.