Feedback Stabilization over Commutative Rings: The Matrix Case

1994 ◽  
Vol 32 (6) ◽  
pp. 1675-1695 ◽  
Author(s):  
V. R. Sule
Keyword(s):  
Commutative Rings ◽  
Feedback Stabilization ◽  
The Matrix ◽  
Matrix Case

Triangular representations of linear algebras

1953 ◽  
Vol 49 (4) ◽  
pp. 595-600 ◽  
Author(s):  
M. P. Drazin
Keyword(s):  
Commutative Algebra ◽  
Similarity Transformation ◽  
Closed Field ◽  
Triangular Form ◽  
Algebraically Closed Field ◽  
Matrix Algebras ◽  
Common Eigenvector ◽  
General Systems ◽  
The Matrix ◽  
Matrix Case

It is well known that the elements of any given commutative algebra (and hence of any commutative set) of n × n matrices, over an algebraically closed field K, have a common eigenvector over K; indeed, the elements of such an algebra can be simultaneously reduced to triangular form (by a suitable similarity transformation). McCoy (5) has shown that a triangular reduction is always possible even for matrix algebras satisfying a condition substantially weaker than commutativity. Our aim in this note is to extend these results to more general systems (our arguments being, incidentally, simpler than some used for the matrix case even by writers subsequent to McCoy).

scholarly journals Noncommutative homogeneous spaces: The matrix case

2012 ◽  
Vol 62 (6) ◽  
pp. 1451-1466 ◽  
Author(s):  
Teodor Banica ◽  
Adam Skalski ◽  
Piotr Sołtan
Keyword(s):  
Homogeneous Spaces ◽  
The Matrix ◽  
Matrix Case

scholarly journals The Matrix Linear Unilateral and Bilateral Equations with Two Variables over Commutative Rings

ISRN Algebra ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
N. S. Dzhaliuk ◽  
V. M. Petrychkovych
Keyword(s):  
Linear Equations ◽  
Standard Form ◽  
Commutative Rings ◽  
Matrix Equations ◽  
General Solutions ◽  
Particular Solutions ◽  
The Matrix ◽  
Bezout Domains

The method of solving matrix linear equations and over commutative Bezout domains by means of standard form of a pair of matrices with respect to generalized equivalence is proposed. The formulas of general solutions of such equations are deduced. The criterions of uniqueness of particular solutions of such matrix equations are established.

Global optimization based on TT-decomposition

2020 ◽  
Vol 35 (4) ◽  
pp. 247-261
Author(s):  
Dmitry Zheltkov ◽  
Eugene Tyrtyshnikov
Keyword(s):  
Global Optimization ◽  
High Accuracy ◽  
Global Optimum ◽  
Stochastic Methods ◽  
The Matrix ◽  
Matrix Case

AbstractIn contrast to many other heuristic and stochastic methods, the global optimization based on TT-decomposition uses the structure of the optimized functional and hence allows one to obtain the global optimum in some problem faster and more reliable. The method is based on the TT-cross method of interpolation of tensors. In this case, the global optimum can be found in practice even in the case when the approximation of the tensor does not possess a high accuracy. We present a detailed description of the method and its justification for the matrix case and rank-1 approximation.

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