EP properties of (b, c)-invertible matrices

2020 ◽  
pp. 1-7
Author(s):  
Michael P. Drazin
Keyword(s):  
Invertible Matrices

scholarly journals A $q$-Analogue of de Finetti's Theorem

10.37236/167 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Alexander Gnedin ◽  
Grigori Olshanski
Keyword(s):  
Boundary Problem ◽  
Galois Field ◽  
Infinite Group ◽  
Natural Action ◽  
De Finetti’S Theorem ◽  
De Finetti's Theorem ◽  
Invertible Matrices

A $q$-analogue of de Finetti's theorem is obtained in terms of a boundary problem for the $q$-Pascal graph. For $q$ a power of prime this leads to a characterisation of random spaces over the Galois field ${\Bbb F}_q$ that are invariant under the natural action of the infinite group of invertible matrices with coefficients from ${\Bbb F}_q$.

scholarly journals On the structure of least common multiple matrices from some class of matrices

2018 ◽  
Vol 10 (1) ◽  
pp. 179-184
Author(s):  
A.M. Romaniv
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Smith Normal Form ◽  
Least Common Multiple ◽  
The Matrix ◽  
Singular Matrices ◽  
Class Of Matrices ◽  
Smith Normal Forms ◽  
Invertible Matrices ◽  
Principal Ideal Domains

For non-singular matrices with some restrictions, we establish the relationships between Smith normal forms and transforming matrices (a invertible matrices that transform the matrix to its Smith normal form) of two matrices with corresponding matrices of their least common right multiple over a commutative principal ideal domains. Thus, for such a class of matrices, given answer to the well-known task of M. Newman. Moreover, for such matrices, received a new method for finding their least common right multiple which is based on the search for its Smith normal form and transforming matrices.

Note on invertible matrices over commutative semirings

2015 ◽  
Vol 64 (3) ◽  
pp. 477-483 ◽  
Author(s):  
Ya-lin Liao ◽  
Xue-ping Wang
Keyword(s):  
Invertible Matrices

scholarly journals Young measures supported on invertible matrices

2013 ◽  
Vol 93 (1) ◽  
pp. 105-123 ◽  
Author(s):  
Barbora Benešová ◽  
Martin Kružík ◽  
Gabriel Pathó
Keyword(s):  
Young Measures ◽  
Invertible Matrices

scholarly journals A diffusion model for Bookstein triangle shape

1996 ◽  
Vol 28 (02) ◽  
pp. 334-335
Author(s):  
Wilfrid S. Kendall
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Hyperbolic Plane ◽  
Negative Curvature ◽  
General Linear Group ◽  
Shape Space ◽  
Shape Theory ◽  
Independent Brownian Motion ◽  
Invertible Matrices

This reports on work in progress, developing a dynamical context for Bookstein's shape theory. It shows how Bookstein's shape space for triangles arises when the landmarks are moved around by a particular Brownian motion on the general linear group of (2 × 2) invertible matrices. Indeed, suppose that the random process G(t) ∈ GL(2, ℝ) solves the Stratonovich stochastic differential equation dsG = (dsB)G for a Brownian matrix B (independent Brownian motion entries). If {x1 x2, x3 } is a fixed (non-degenerate) triple of planar points then Xi(t) = G(t)xi ; determines a triple {X1 X2, X3 } whose shape performs a diffusion which can be shown to be Brownian motion on the hyperbolic plane of negative curvature − 2.

Matrices as Sums of Invertible Matrices

1987 ◽  
Vol 60 (1) ◽  
pp. 33-35
Author(s):  
N. J. Lord
Keyword(s):  
Invertible Matrices

A key exchange protocol using matrices over group ring

2019 ◽  
Vol 12 (05) ◽  
pp. 1950075
Author(s):  
Indivar Gupta ◽  
Atul Pandey ◽  
Manish Kant Dubey
Keyword(s):  
Group Ring ◽  
Complexity Analysis ◽  
Discrete Logarithm ◽  
Key Exchange ◽  
Group Rings ◽  
Secret Key ◽  
Key Exchange Protocol ◽  
Diffie Hellman ◽  
Shared Secret ◽  
Invertible Matrices

The first published solution to key distribution problem is due to Diffie–Hellman, which allows two parties that have never communicated earlier, to jointly establish a shared secret key over an insecure channel. In this paper, we propose a new key exchange protocol in a non-commutative semigroup over group ring whose security relies on the hardness of Factorization with Discrete Logarithm Problem (FDLP). We have also provided its security and complexity analysis. We then propose a ElGamal cryptosystem based on FDLP using the group of invertible matrices over group rings.

Sign in / Sign up

Export Citation Format

Share Document