Zobrazeno 1 - 10
of 230
pro vyhledávání: '"Sergeichuk, Vladimir V."'
Autor:
Borges, Victor Senoguchi, Kashuba, Iryna, Sergeichuk, Vladimir V., Sodré, Eduardo Ventilari, Zaidan, André
Publikováno v:
Linear Algebra Appl. 611 (2021) 118-134
We classify all linear operators $A:V\to V$ satisfying $(Au,v)=(u,A^rv)$ and all linear operators satisfying $(Au,A^rv)=(u,v)$ with $r=2,3,\dots$ on a complex, real, or quaternion vector space with scalar product given by a nonsingular symmetric, ske
Externí odkaz:
http://arxiv.org/abs/2012.04052
Autor:
Bondarenko, Vitalij M., Futorny, Vyacheslav, Petravchuk, Anatolii P., Sergeichuk, Vladimir V.
Publikováno v:
Linear Algebra and its Applications 612 (2021) 188-205
I.M. Gelfand and V.A. Ponomarev (1969) proved that the problem of classifying pairs (A,B) of commuting nilpotent operators on a vector space contains the problem of classifying an arbitrary t-tuple of linear operators. Moreover, it contains the probl
Externí odkaz:
http://arxiv.org/abs/2012.04038
Publikováno v:
Linear Algebra Appl. 609 (2021) 317-331
Two matrix vector spaces $V,W\subset \mathbb C^{n\times n}$ are said to be equivalent if $SVR=W$ for some nonsingular $S$ and $R$. These spaces are congruent if $R=S^T$. We prove that if all matrices in $V$ and $W$ are symmetric, or all matrices in $
Externí odkaz:
http://arxiv.org/abs/2009.13894
Autor:
Bovdi, Victor A., Klymchuk, Tetiana, Rybalkina, Tetiana, Salim, Mohamed A., Sergeichuk, Vladimir V.
Publikováno v:
Linear Algebra Appl. 596 (2020) 82-105
We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces and linear
Externí odkaz:
http://arxiv.org/abs/2003.06919
Publikováno v:
Linear Algebra Appl. 587 (2020) 92-110
Let $V$ be a vector space over a field $\mathbb F$ with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If $\mathbb F=\mathbb C$, then we give canonical matrices of isometric and selfadjoint operators
Externí odkaz:
http://arxiv.org/abs/1911.04993
Our purpose is to give new proofs of several known results about perturbations of matrix pencils. Andrzej Pokrzywa (1986) described the closure of orbit of a Kronecker canonical pencil $A-\lambda B$ in terms of inequalities with pencil invariants. In
Externí odkaz:
http://arxiv.org/abs/1907.03213
Publikováno v:
Linear Algebra Appl. 573 (2019) 26-36
Let G be a graph with undirected and directed edges. Its representation is given by assigning a vector space to each vertex, a bilinear form on the corresponding vector spaces to each directed edge, and a linear map to each directed edge. Two represe
Externí odkaz:
http://arxiv.org/abs/1903.10386
Publikováno v:
Linear Algebra Appl. 566 (2019) 212-244
In representation theory, a classification problem is called wild if it contains the problem of classifying matrix pairs up to simultaneous similarity. The latter problem is considered as hopeless; it contains the problem of classifying an arbitrary
Externí odkaz:
http://arxiv.org/abs/1810.09219
Publikováno v:
Linear Algebra and Its Applications 537 (2018) 84-99
Let $\mathbb F$ be a field of characteristic not $2$, and let $(A,B)$ be a pair of $n\times n$ matrices over $\mathbb F$, in which $A$ is symmetric and $B$ is skew-symmetric. A canonical form of $(A,B)$ with respect to congruence transformations $(S^
Externí odkaz:
http://arxiv.org/abs/1709.10350
Publikováno v:
Linear Algebra and Its Applications 536 (2018) 201-209
For each two-dimensional vector space $V$ of commuting $n\times n$ matrices over a field $\mathbb F$ with at least 3 elements, we denote by $\widetilde V$ the vector space of all $(n+1)\times(n+1)$ matrices of the form $\left[\begin{smallmatrix}A&*\\
Externí odkaz:
http://arxiv.org/abs/1709.10334