相关论文: Applications of the duality method to generalizati…

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

Let $K$ be a field (finite or infinite) of char$(K)\neq 2$ and let $UT_n=UT_n(K)$ be the $n\times n$ upper triangular matrix algebra over $K$. If $\cdot $ is the usual product on $UT_n$ then with the new product $a\circ b=(1/2)(a\cdot b…

In this paper, $\mathcal{P}$-canonical forms of $(A^{k})_{k}$ (or simply of the matrix $A$) are defined and some of their properties are proved. It is also shown how we can deduce from them many interesting informations about the matrix…

Symmetries in the Lagrangian formalism of arbitrary order are analysed with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second order equations and a scalar field we establish a polynomial structure in the…

Structured canonical forms under unitary and suitable structure-preserving similarity transformations for normal and (skew-)Hamiltonian as well as normal and per(skew)-Hermitian matrices are proposed. Moreover, an algorithm for computing…

In this paper the problem of finding a normal form of triangles and plane quadrilaterals up to similarity is considered. Several normal forms for triangles and a normal form for quadrilaterals of special case are described. Normal forms of…

We give the definition of a duality that is applicable to arbitrary $k$-forms. The operator that defines the duality depends on a fixed form $\Omega$. Our definition extends in a very natural way the Hodge duality of $n$-forms in $2n$…

We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.

Let $J_r$ denote a full $r \times r$ Jordan block matrix with eigenvalue $1$ over a field $F$ of characteristic $p$. For positive integers $r$ and $s$ with $r \leq s$, the Jordan canonical form of the $r s \times r s$ matrix $J_{r} \otimes…

The $R_h^{j_1;j_2}$ matrices of the Jordanian U$_h$(sl(2)) algebra at arbitrary dimensions may be obtained from the corresponding $R_q^{j_1;j_2}$ matrices of the standard $q$-deformed U$_q$(sl(2)) algebra through a contraction technique. By…

In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on…

Let $A$ be an algebra and let $X$ be an $A$-bimodule. A $\Bbb C-$linear mapping $d:A \to X$ is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) $\delta:A \to X$ such that…

There are two ways to compute Poincar\'e-Dulac normal forms of systems of ODEs. Under the original approach used by Poincar\'e the normalizing transformation is explicitly computed. On each step, the normalizing procedure requires the…

We apply the quaternionic Jordan form to classify the hypercomplex nilpotent almost abelian Lie algebras in all dimensions and to carry out the complete classification of 12-dimensional hypercomplex almost abelian Lie algebras. Moreover, we…

We consider a large class of matrix problems, which includes the problem of classifying arbitrary systems of linear mappings. For every matrix problem from this class, we construct Belitskii's algorithm for reducing a matrix to a canonical…

The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a…

Results on matrix canonical forms are used to give a complete description of the higher rank numerical range of matrices arising from the study of quantum error correction. It is shown that the set can be obtained as the intersection of…

Jordan as well as related triple systems have been used to find several solutions of the Yang-Baxter equation, which are of rational as well as trigonometric type.

A longstanding issue is the classical equivalence between the Jordan and the Einstein frames, which is considered just a field redefinition of the metric tensor and the scalar field. In this work, based on the previous result that the…

We study the relationship between cyclic homology of Jordan superalgebras and second cohomologies of their Tits-Kantor-Koecher Lie superalgebras. In particular, we focus on Jordan superalgebras that are Kantor doubles of bracket algebras.…