Сказка о трех диагонализациях
A tale of three diagonalizations: https://arxiv.org/abs/2009.03990
Howard E. Haber
In addition to the diagonalization of a normal matrix by a unitary similarity transformation, there are two other types of diagonalization procedures that sometimes arise in quantum theory applications---the singular value decomposition and the Autonne-Takagi factorization. In these pedagogical notes, we carry out each of these diagonalization procedures for the most general 2×2 matrices for which the corresponding diagonalization is possible and provide explicit analytical results in each of the three cases.
Comments: 27 pages
Howard E. Haber
In addition to the diagonalization of a normal matrix by a unitary similarity transformation, there are two other types of diagonalization procedures that sometimes arise in quantum theory applications---the singular value decomposition and the Autonne-Takagi factorization. In these pedagogical notes, we carry out each of these diagonalization procedures for the most general 2×2 matrices for which the corresponding diagonalization is possible and provide explicit analytical results in each of the three cases.
Comments: 27 pages