Simultaneous block diagonalization of matrices of finite order. (2nd February 2021)

• Record Type: Journal Article
• Authors: Bischer, Ingolf; Döring, Christian; Trautner, Andreas
• Is Part Of: Journal of physics. Volume 54:Number 8(2021)
• Publication Date: 2021-02-02
• Subjects: invariant subspace -- block diagonal matrix -- group theory -- simultaneous matrix transformation -- CP-transformation -- fundamental symmetries -- non-linearly realized discrete symmetries; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/abd979
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we give an efficient algorithm to explicitly compute a transfer matrix which realizes the simultaneous block diagonalization of unitary matrices whose decomposition in irreducible blocks (common invariant subspaces) is known from elsewhere. Our main motivation lies in particle physics, where the resulting transfer matrix must be known explicitly in order to unequivocally determine the action of outer automorphisms such as parity, charge conjugation, or time reversal on the particle spectrum.