Maximize the Dimension of the Null Space of $A-aI$.The zero matrix is a diagonal matrix, and thus it is diagonalizable. Is every diagonalizable matrix invertible? Every Diagonalizable Matrix is Invertible For each eigenvalue $\lambda$ of $A$, find a basis of the eigenspace $E_įor this problem, you may use the fact that both matrices have the same characteristic.Find eigenvalues $\lambda$ of the matrix $A$ and their algebraic multiplicities from the characteristic polynomial $p(t)$.
Let $A$ be the $n\times n$ matrix that you want to diagonalize (if possible). A concrete example is provided below, and several exercise problems are presented at the end of the post. The process can be summarized as follows. We only describe the procedure of diagonalization, and no justification will be given. Here we explain how to diagonalize a matrix.
