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A transvection decomposition in GL(n,2)

Clorinda De Vivo, Claudia Metelli (2002)

Colloquium Mathematicae

An algorithm is given to decompose an automorphism of a finite vector space over ℤ₂ into a product of transvections. The procedure uses partitions of the indexing set of a redundant base. With respect to tents, i.e. finite ℤ₂-representations generated by a redundant base, this is a decomposition into base changes.

A treatment of a determinant inequality of Fiedler and Markham

Minghua Lin (2016)

Czechoslovak Mathematical Journal

Fiedler and Markham (1994) proved det H ^ k k ≥ det H , where H = ( H i j ) i , j = 1 n is a positive semidefinite matrix partitioned into n × n blocks with each block k × k and H ^ = ( tr H i j ) i , j = 1 n . We revisit this inequality mainly using some terminology from quantum information theory. Analogous results are included. For example, under the same condition, we prove det ( I n + H ^ ) ≥ det ( I n k + k H ) 1 / k .

A tutorial on conformal groups

Ian Porteous (1996)

Banach Center Publications

Our concern is with the group of conformal transformations of a finite-dimensional real quadratic space of signature (p,q), that is one that is isomorphic to ℝ p , q , the real vector space ℝ p + q , furnished with the quadratic form x ( 2 ) = x · x = - x 1 2 - x 2 2 - . . . - x p 2 + x p + 1 2 + . . . + x p + q 2 , and especially with a description of this group that involves Clifford algebras.

A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition

Sébastien Pernet (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation.

Abelian differential modes are quasi-affine

David Stanovský (2012)

Commentationes Mathematicae Universitatis Carolinae

We study a class of strongly solvable modes, called differential modes. We characterize abelian algebras in this class and prove that all of them are quasi-affine, i.e., they are subreducts of modules over commutative rings.

Absolute value equations with tensor product structure: Unique solvability and numerical solution

Somayeh Mollahasani, Fatemeh Panjeh Ali Beik (2022)

Applications of Mathematics

We consider the absolute value equations (AVEs) with a certain tensor product structure. Two aspects of this kind of AVEs are discussed in detail: the solvability and approximate solution. More precisely, first, some sufficient conditions are provided which guarantee the unique solvability of this kind of AVEs. Furthermore, a new iterative method is constructed for solving AVEs and its convergence properties are investigated.  The validity of established theoretical results and performance of the...

Absolutely flat idempotents.

Johnson, Charles R., Harel, Yonatan, Hillar, Christopher J., Groves, Jonathan M., Rault, Patrick X. (2003)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Currently displaying 221 – 240 of 393