A tale of three diagonalizations
Abstract
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 applicationsthe singular value decomposition and the AutonneTakagi factorization. In these pedagogical notes, we carry out each of these diagonalization procedures for the most general $2\times 2$ matrices for which the corresponding diagonalization is possible and provide explicit analytical results in each of the three cases.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 arXiv:
 arXiv:2009.03990
 Bibcode:
 2020arXiv200903990H
 Keywords:

 High Energy Physics  Phenomenology;
 Quantum Physics
 EPrint:
 27 pages