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

scholarly journals НАСЛЕДОВАНИЕ СИНГУЛЯРНЫХ ВЕКТОРОВ ПРИ ПОПОЛНЕНИИ МАТРИЦЫ СТОЛБЦОМ

2021 ◽  
Vol 6 (12(81)) ◽  
pp. 36-40
Author(s):  
В. Кутрунов ◽  
Т. Латфуллин
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Symmetric Matrices ◽  
Singular Vectors ◽  
The Matrix ◽  
Singular Value Decompositions ◽  
Singular Numbers ◽  
The Right ◽  
Value Decomposition

Let the matrix A1 be obtained from the matrix A by adding a column to it on the right. The possibility of inheritance of singular numbers and the corresponding singular vectors when passing from matrix A to matrix A1 is investigated. The singular value decompositions of the matrix A are based on the scalar and vector properties of the square symmetric matrices ATA and AAT. The article deals with the singular value decomposition of the matrix A, which has more rows than columns, and the decomposition is based on the analysis of the ATA matrix.

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.

Improving TF-IDF with Singular Value Decomposition (SVD) for Feature Extraction on Twitter

2017 ◽  
Author(s):  
Ammar Ismael Kadhim ◽  
Yu-N Cheah ◽  
Inaam Abbas Hieder ◽  
Rawaa Ahmed Ali
Keyword(s):  
Feature Extraction ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Value Decomposition
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