scholarly journals Structure preserving stratification of skew-symmetric matrix polynomials

2017 ◽  
Vol 532 ◽  
pp. 266-286 ◽  
Author(s):  
Andrii Dmytryshyn
Keyword(s):  
Symmetric Matrix ◽  
Structure Preserving ◽  
Matrix Polynomials ◽  
Skew Symmetric Matrix

scholarly journals Skew-symmetric matrix polynomials and their Smith forms

2013 ◽  
Vol 438 (12) ◽  
pp. 4625-4653 ◽  
Author(s):  
D. Steven Mackey ◽  
Niloufer Mackey ◽  
Christian Mehl ◽  
Volker Mehrmann
Keyword(s):  
Symmetric Matrix ◽  
Matrix Polynomials ◽  
Skew Symmetric Matrix

scholarly journals Overlapping Pfaffians

10.37236/1263 ◽  
1995 ◽  
Vol 3 (2) ◽  
Author(s):  
Donald E. Knuth
Keyword(s):  
Symmetric Matrix ◽  
History Of ◽  
Combinatorial Construction ◽  
Skew Symmetric Matrix

A combinatorial construction proves an identity for the product of the Pfaffian of a skew-symmetric matrix by the Pfaffian of one of its submatrices. Several applications of this identity are followed by a brief history of Pfaffians.

scholarly journals Generic Symmetric Matrix Polynomials with Bounded Rank and Fixed Odd Grade

2020 ◽  
Vol 41 (3) ◽  
pp. 1033-1058
Author(s):  
Fernando De Terán ◽  
Andrii Dmytryshyn ◽  
Froilán M. Dopico
Keyword(s):  
Symmetric Matrix ◽  
Matrix Polynomials ◽  
Bounded Rank

DECOMPOSITION OF STOCHASTIC FLOWS AND ROTATION MATRIX

2002 ◽  
Vol 02 (01) ◽  
pp. 93-107 ◽  
Author(s):  
PAULO R. C. RUFFINO
Keyword(s):  
Asymptotic Behaviour ◽  
Constant Curvature ◽  
Symmetric Matrix ◽  
Rotation Matrix ◽  
Stochastic Flow ◽  
Stochastic Flows ◽  
Affine Transformations ◽  
Simply Connected ◽  
Skew Symmetric Matrix

We provide geometrical conditions on the manifold for the existence of the Liao's factorization of stochastic flows [10]. If M is simply connected and has constant curvature, then this decomposition holds for any stochastic flow, conversely, if every flow on M has this decomposition, then M has constant curvature. Under certain conditions, it is possible to go further on the factorization: φt = ξt°Ψt° Θt, where ξt and Ψt have the same properties of Liao's decomposition and (ξt°Ψt) are affine transformations on M. We study the asymptotic behaviour of the isometric component ξt via rotation matrix, providing a Furstenberg–Khasminskii formula for this skew-symmetric matrix.

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