A tale of three diagonalizations
High Energy Physics - Phenomenology
2021-02-26 v3 Quantum Physics
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 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 matrices for which the corresponding diagonalization is possible and provide explicit analytical results in each of the three cases.
Cite
@article{arxiv.2009.03990,
title = {A tale of three diagonalizations},
author = {Howard E. Haber},
journal= {arXiv preprint arXiv:2009.03990},
year = {2021}
}
Comments
27 pages; version 2 adds a footnote 14 and improves the pdf output by modifying the implementation of hyperref; version 3 corrects an error in eq. (78)