A hollow matrix is a matrix that contains mostly zero entries, with only a few non-zero entries. These non-zero entries are usually located along the diagonal of the matrix.
Diagonalization is a process of finding a diagonal matrix that is similar to the given matrix. This means that the two matrices have the same eigenvalues and eigenvectors.
Diagonalization is important because it simplifies calculations involving matrices. It also allows us to easily find powers of matrices and solve systems of linear equations.
To diagonalize a matrix, we need to find its eigenvalues and eigenvectors. Then, we can use these eigenvectors to form a diagonal matrix and find the matrix similarity transformation that will convert the given matrix into its diagonal form.
No, not all matrices can be diagonalized. A matrix can only be diagonalized if it has a full set of linearly independent eigenvectors. If the matrix does not have enough eigenvectors, it cannot be diagonalized.