A tale of three diagonalizations

International Journal of Modern Physics A ◽

10.1142/s0217751x21300027 ◽

2021 ◽

pp. 2130003

Author(s):

Howard E. Haber

Keyword(s):

Quantum Theory ◽

Singular Value Decomposition ◽

General Formula ◽

Similarity Transformation ◽

Singular Value ◽

Normal Matrix ◽

Unitary Similarity ◽

Unitary Similarity Transformation ◽

Takagi Factorization ◽

Value Decomposition

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 this pedagogical review, each of these diagonalization procedures is performed for the most general [Formula: see text] matrices for which the corresponding diagonalization is possible, and explicit analytical results are provided in each of the three cases.

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Singular value decomposition for the Takagi factorization of symmetric matrices

Applied Mathematics and Computation ◽

10.1016/j.amc.2014.01.170 ◽

2014 ◽

Vol 234 ◽

pp. 380-384 ◽

Cited By ~ 3

Author(s):

Alexander M. Chebotarev ◽

Alexander E. Teretenkov

Keyword(s):

Singular Value Decomposition ◽

Singular Value ◽

Symmetric Matrices ◽

Takagi Factorization ◽

Value Decomposition

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Field-oriented modelling for a two-phase axial-flux brushless motor in a direct-drive electric vehicle by using similarity transformation and singular value decomposition methods

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1243/09596518jsce694 ◽

2009 ◽

Vol 223 (5) ◽

pp. 633-646

Author(s):

J-L Kuo ◽

K-L Chao

Keyword(s):

Singular Value Decomposition ◽

Electric Vehicle ◽

Similarity Transformation ◽

Singular Value ◽

Direct Drive ◽

Axial Flux ◽

Two Phase ◽

Brushless Motor ◽

Modelling Techniques ◽

Value Decomposition

Modelling techniques are proposed for describing a two-phase axial-flux brushless motor in a direct-drive electric vehicle. Similarity transformation and singular value decomposition (ST-SVD) methods are used to linearize the system model. Stationary and cosecant coordinate models are derived on the basis of the methods proposed. Decoupled inductances and constant torque relations are also obtained. The model proposed is a very useful aid in describing the system dynamics. Simulation and experimental results are illustrated to verify the validity of the model. The given system modelling techniques can provide valuable mathematical models for associated vector control.

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