takagi factorization
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ZND-ZeaD Models and Theoretics Including Proofs for Takagi Factorization of Complex Time-Dependent Symmetric Matrix

2021 ◽  
Author(s):  
Zhuosong Fu ◽  
Min Yang ◽  
Jinjin Guo ◽  
Jianrong Chen ◽  
Yunong Zhang
Keyword(s):  
Symmetric Matrix ◽  
Time Dependent ◽  
Complex Time ◽  
Takagi Factorization

scholarly journals A tale of three diagonalizations

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.

Partial orthogonal rank-one decomposition of complex symmetric tensors based on the Takagi factorization

2018 ◽  
Vol 332 ◽  
pp. 56-71 ◽  
Author(s):  
Xuezhong Wang ◽  
Maolin Che ◽  
Yimin Wei
Keyword(s):  
Symmetric Tensors ◽  
Rank One ◽  
Complex Symmetric ◽  
Takagi Factorization

Bloch-Messiah reduction of Gaussian unitaries by Takagi factorization

2016 ◽  
Vol 94 (6) ◽  
Author(s):  
Gianfranco Cariolaro ◽  
Gianfranco Pierobon
Keyword(s):  
Takagi Factorization

Singular value decomposition for the Takagi factorization of symmetric matrices

2014 ◽  
Vol 234 ◽  
pp. 380-384 ◽  
Author(s):  
Alexander M. Chebotarev ◽  
Alexander E. Teretenkov
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Symmetric Matrices ◽  
Takagi Factorization ◽  
Value Decomposition

A generalization of the complex Autonne–Takagi factorization to quaternion matrices

2012 ◽  
Vol 60 (11-12) ◽  
pp. 1239-1244 ◽  
Author(s):  
Roger A. Horn ◽  
Fuzhen Zhang
Keyword(s):  
Quaternion Matrices ◽  
Takagi Factorization

scholarly journals A Divide-and-Conquer Method for the Takagi Factorization

2008 ◽  
Vol 30 (1) ◽  
pp. 142-153 ◽  
Author(s):  
Wei Xu ◽  
Sanzheng Qiao
Keyword(s):  
Divide And Conquer ◽  
Takagi Factorization
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