Results 11 to 20 of about 2,610,164 (335)
Rings over which the transpose of every invertible matrix is invertible
Journal of Algebra, 2009 We prove that the transpose of every invertible square matrix over a ring R is invertible if and only if R/rad(R) is commutative. Many other characterizations are obtained for such rings R in terms of U(R) (the group of units of R), including, for instance, c+ba∈U(R)⇒c+ab∈U(R), and 1+abc−cba∈U(R) (for all a,b,c∈R).
Ram Niwas Gupta +3 more
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Effect of Self-Invertible Matrix on Cipher Hexagraphic Polyfunction [PDF]
Cryptography, 2019 A cryptography system was developed previously based on Cipher Polygraphic Polyfunction transformations, C i × j ( t ) ≡ A i × i t P i × j m o d N where C i × j , P i × j , A i
Sally Lin Pei Ching, Faridah Yunos
doaj +3 more sources
Extension problem to an invertible matrix [PDF]
Proceedings of the American Mathematical Society, 1993 The extension problem for rectangular matrices with values in Banach algebra to an invertible square matrix is investigated. For this problem to be solvable for a matrix D , the following condition is necessary: for every maximal ideal m of the algebra ...
V. A. Tolokonnikov
semanticscholar +3 more sources
Analytic roots of invertible matrix functions
The Electronic Journal of Linear Algebra, 2005 Various conditions are developed that guarantee existence of analytic roots of a given analytic matrix function withinvertible values defined on a simply connected domain.
Leiba Rodman, Ilya M. Spitkovsky
semanticscholar +5 more sources
Every invertible matrix is diagonally equivalent to a matrix with distinct eigenvalues
Linear Algebra and its Applications, 2012 AbstractWe show that for every invertible n×n complex matrix A there is an n×n diagonal invertible D such that AD has distinct eigenvalues. Using this result, we affirm a conjecture of Feng, Li, and Huang that an n×n matrix is not diagonally equivalent to a matrix with distinct eigenvalues if and only if it is singular and all its principal minors of ...
Zejun Huang +3 more
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Efficient Tensor Robust Principal Analysis via Right-Invertible Matrix-Based Tensor Products
AxiomsIn this paper, we extend the definition of tensor products from using an invertible matrix to utilising right-invertible matrices, exploring the algebraic properties of these new tensor products.
Zhang Huang, Jun Feng, Wei Li
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Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space [PDF]
SciPost PhysicsWe discuss the exact non-invertible Kramers-Wannier symmetry of 1+1d lattice models on a tensor product Hilbert space of qubits. This symmetry is associated with a topological defect and a conserved operator, and the latter can be presented as a matrix ...
Nathan Seiberg, Sahand Seifnashri, Shu-Heng Shao
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Image Encryption Algorithm Based on the H-Fractal and Dynamic Self-Invertible Matrix. [PDF]
Comput Intell Neurosci, 2019 In this paper, an image encryption algorithm based on the H-fractal and dynamic self-invertible matrix is proposed. The H-fractal diffusion encryption method is firstly used in this encryption algorithm. This method crosses the pixels at both ends of the
Zhang X, Wang L, Niu Y, Cui G, Geng S.
europepmc +2 more sources
An Efficient Algorithm for Inverting a Block-Symmetric Matrix [PDF]
Mathematics of Computation, 1967 S. Charmonman
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The asymptotic probability that a random biased matrix is invertible
Discrete Mathematics, 1990 AbstractLet q = pe be a power of a prime. Suppose we are given a probability distribution on GF(q) not concentrated on any proper affine subspace of GF(q) regarded as a vector space over its prime subfield GF(p). Let M be a random n by n matrix whose entries are chosen independently from the given distribution and let An be the probability that M is ...
H. D. Rees +2 more
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