Matrix Diagonalization

Determine if a given matrix is diagonalizable and, if so, diagonalize it.

Diagonalization is an essential concept in linear algebra that finds application in various fields such as differential equations, quantum mechanics, and computer graphics. At the heart of this process is the problem of determining whether a square matrix can be transformed into a diagonal matrix, which is often easier to work with. This involves finding a basis composed entirely of eigenvectors of the matrix, allowing the linear transformation represented by the matrix to be expressed in its simplest form.