Matrix Decompositions

2021 ◽  
pp. 167-295
Author(s):  
Nathaniel Johnston
Keyword(s):  
Matrix Decompositions

Polarimetry of soil and vegetation in the visible II: Mueller matrix decompositions

2021 ◽  
pp. 107622
Author(s):  
Sergey N. Savenkov ◽  
Alexander A. Kohkanovsky ◽  
Evgen A. Oberemok ◽  
Ivan S. Kolomiets ◽  
Alexander S. Klimov
Keyword(s):  
Mueller Matrix ◽  
Matrix Decompositions

scholarly journals Extracting commuting patterns in railway networks through matrix decompositions

2014 ◽  
Author(s):  
Shashank Jere ◽  
Justin Dauwels ◽  
Muhammad Tayyab Asif ◽  
Nikola Mitro Vie ◽  
Andrzej Cichocki ◽  
...  
Keyword(s):  
Matrix Decompositions ◽  
Railway Networks ◽  
Commuting Patterns

scholarly journals Sparse matrix decompositions and graph characterizations

2012 ◽  
Vol 437 (3) ◽  
pp. 932-947 ◽  
Author(s):  
Kshitij Khare ◽  
Bala Rajaratnam
Keyword(s):  
Sparse Matrix ◽  
Matrix Decompositions

scholarly journals A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 893
Author(s):  
Yunlan Wei ◽  
Yanpeng Zheng ◽  
Zhaolin Jiang ◽  
Sugoog Shon
Keyword(s):  
Toeplitz Matrices ◽  
Schur Complement ◽  
Matrix Transformations ◽  
Matrix Decompositions ◽  
Mersenne Numbers

In this paper, we study periodic tridiagonal Toeplitz matrices with perturbed corners. By using some matrix transformations, the Schur complement and matrix decompositions techniques, as well as the Sherman-Morrison-Woodbury formula, we derive explicit determinants and inverses of these matrices. One feature of these formulas is the connection with the famous Mersenne numbers. We also propose two algorithms to illustrate our formulas.

scholarly journals Common Factors in Fraction-Free Matrix Decompositions

2020 ◽  
Author(s):  
Johannes Middeke ◽  
David J. Jeffrey ◽  
Christoph Koutschan
Keyword(s):  
Normal Form ◽  
Common Factors ◽  
Reduction Process ◽  
Triangular Matrices ◽  
Specific Data ◽  
Matrix Decompositions ◽  
The Matrix ◽  
The Common

AbstractWe consider LU and QR matrix decompositions using exact computations. We show that fraction-free Gauß–Bareiss reduction leads to triangular matrices having a non-trivial number of common row factors. We identify two types of common factors: systematic and statistical. Systematic factors depend on the reduction process, independent of the data, while statistical factors depend on the specific data. We relate the existence of row factors in the LU decomposition to factors appearing in the Smith–Jacobson normal form of the matrix. For statistical factors, we identify some of the mechanisms that create them and give estimates of the frequency of their occurrence. Similar observations apply to the common factors in a fraction-free QR decomposition. Our conclusions are tested experimentally.

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