Diagonalized matrix is to simplify the original matrix into a diagonal matrix that is easier to understand and handle through a series of linear transformations. We need to find an invertible square p so that M=PDP- 1.

Eigenvector sum diagonalization

A matrix can be diagonalized if and only if it has n linearly unrelated eigenvectors. Eigenvector refers to a vector that only expands and contracts without changing its direction under linear transformation. By solving the eigenvector, we can get the diagonalized matrix.

Definition of diagonal matrix

Diagonal matrix refers to a matrix with non-zero elements only on the main diagonal. Diagonal matrix is characterized by simple calculation and easy handling. By diagonalization, the original matrix can be transformed into diagonal matrix, so that the matrix can be better understood and processed.