Diagonalize is a term that refers to the process of converting a matrix into a diagonal matrix, where the only non-zero elements are found on the main diagonal. There are several synonyms for diagonalize, including diagonalize, diagonalization, and diagonalizing. Other terms that can be used to describe the diagonalization process include triangularization, eigenvalue decomposition, and spectral decomposition. These terms refer to different methods of diagonalizing a matrix, each with its own set of advantages and disadvantages. Ultimately, the choice of technique depends on the specific matrix being diagonalized and the goals of the analysis.