A tale of three diagonalizations

2020/09/06 by Howard E. Haber · 1 voice · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Matrix Theory and Algorithms #Tensor decomposition and applications #hep-ph #quant-ph

paper · pdf · doi:10.1142/s0217751x21300027

arxiv published 2020/09/06 · openalex created_date 2020/09/14 · openalex publication_date 2021/02/10 · arxiv updated 2021/02/25 · openalex updated_date 2026/07/30

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 2× 2 matrices for which the corresponding diagonalization is possible and provide explicit analytical results in each of the three cases.

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Discussions

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